1. History of Algebraic Topology; Homotopy Equivalence - Pierre Albin

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  • Опубликовано: 23 дек 2024

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  • @crapadopalese
    @crapadopalese 5 лет назад +153

    This guy is so charming and witty. It's like they took a slight-of-hands magician to give a math talk.

    • @TheDavidlloydjones
      @TheDavidlloydjones 6 месяцев назад

      sleight
      Completely different concept.

    • @crapadopalese
      @crapadopalese 6 месяцев назад +1

      @@TheDavidlloydjones Ah, thank you for the correction! English is not my native tongue so it's always good to be made aware of some recurring mistake I've probably made a million times without being corrected :)

  • @llrecova
    @llrecova 5 лет назад +113

    Algebraic topology is one of the most beautiful courses in mathematics.

    • @i_amscarface_the_legend9744
      @i_amscarface_the_legend9744 3 года назад +5

      Really ? I have only general ideas what this of Mathematics is about ! But, u give me motivation to start this course ! Thank u!

  • @murasso2736
    @murasso2736 2 года назад +20

    This guy is one of the rare professors whose classes are enormously exciting

    • @TheDavidlloydjones
      @TheDavidlloydjones 6 месяцев назад

      Yes. Imagine if he transferred his intelligence to making a RUclips video!
      But the back of his head as he scribbles on the blackboard is pretty much like that of every other idjit out there who thinks that's an activity worth recording and rebroadcasting. Just nuts!

  • @johnrickert5572
    @johnrickert5572 3 года назад +16

    Outstanding lecture! Thanks for providing it. At 31:30, one may note that removing any point from the circle leaves a contractible space, while this is not the case with the annulus. Or more simply, the annulus has a nonempty interior, whereas the circle has empty interior.

  • @aeolidida3204
    @aeolidida3204 4 года назад +37

    I really enjoyed your lecture! Thank you for what you are doing. I'm from Russia, and in my university I don't have such a course. I have to work through a lot of material on my own, and your lectures do help me.

    • @intensedeep777
      @intensedeep777 Год назад +1

      me too,i'm from china and my University didn't have these course too:) but my english is very poor......

  • @carloselfrancos7205
    @carloselfrancos7205 Год назад +2

    Best course in algebraic topology so far

  • @duzhu7719
    @duzhu7719 5 лет назад +75

    Can you upload the next semester's Algebraic Topology?Thank you a lot.

  • @JoyLoveLifeSong
    @JoyLoveLifeSong 9 месяцев назад +1

    I wish I could ask questions! Does anyone know about the fundamental relationship between chaos theory and algebraic topology? I never knew chaos theory was necessary for forward movement in topology! Fascinating.

  • @A1B2C3x
    @A1B2C3x Месяц назад

    At 41:30, wouldn't the deformation retraction be f(t): x => (1-t)x so that, according to the definition of a deformation retraction, f(0)=IdX ?

  • @aleksherstyuk8319
    @aleksherstyuk8319 4 года назад +8

    Timestamp 1:02:27 this is really nitpicky, but I think Freedman's result was that there are uncountablely infinitely smooth structures on R4, but it was known that for any n other than 4, there's only 1 unique smooth structure. He said 4 and higher though. The reality is much weirder: R4 is the only exception to the rule that "classifying Rn topologically or smoothly is essentially the same task". (And it's an exception in an unexpected, dramatic, big way)
    Really great lecture! I'm hooked

    • @aleksherstyuk8319
      @aleksherstyuk8319 4 года назад +2

      @Mohammad Maruf Mamun the same thing happened to me. I was a pure algebra and topology (and category theory) guy, but turns out, introducing differential structure just makes certain things mysterious and interesting

  • @maestraccivalentin316
    @maestraccivalentin316 5 лет назад +24

    These are super cool! Waiting for semester 2! :)

  • @sarita5294
    @sarita5294 7 месяцев назад

    It was an awesome lecture with you sir on this channel here, just superb , the funny elements you added in the class were the best part as most professor just focuses only on giving an 1 hour boring lecture just by filling up the board the whole time. We need professors like you in our institutes.

  • @umut3147
    @umut3147 2 года назад

    In 31:52, I think we don't need the dimension theorem. If we subtract two points on S^1 becomes disconnected. However, This isn't the case in Ann.

  • @SanjayaShastry
    @SanjayaShastry 2 месяца назад

    Could you please clarify this doubt? You said that the maximum number of closed curves we can remove without disconnecting the surface is the genus. You also said that it is the first betti number. But, isn't the first betti number of the double torus 4?

  • @candlemelt
    @candlemelt Год назад +120

    Am I watching this because a guy on tiktok said it was hard? Yes💀

  • @pedromatzke2088
    @pedromatzke2088 5 лет назад +12

    Pierre Albin was right to have some doubts, Mittag-Leffler is from Sweden not Norway.

    • @12maritere
      @12maritere 3 года назад +3

      Up to 1905 Norway and Sweden were the same kingdom, so he was right

  • @Sidionian
    @Sidionian 3 года назад +3

    Why hasn't Semester 2 been uploaded!?

  • @SreeRama_20
    @SreeRama_20 2 года назад +3

    thanks from India please upload some more topics like complex analysis, functional analysis

  • @9Glaedr0
    @9Glaedr0 7 месяцев назад

    This is fun to hear. But I don't understand a thing. Where do I do a foundation course?

  • @AkamiChannel
    @AkamiChannel 11 месяцев назад

    Anywhere online to find the supplements he's referring to?

  • @DannyWitwer
    @DannyWitwer Год назад

    For me these are the most inciting lectures in the subject. Thank you, Professor Pierre Albin! And I am really eager to ask, are there videos of the second semester yet?

  • @spacetimemalleable7718
    @spacetimemalleable7718 2 года назад +2

    A GREAT lecture! Most impressed by his knowledge and wit.

  • @alessandragnecchi8767
    @alessandragnecchi8767 4 года назад +10

    when you're enjoying the nice introduction and then 8:38 arrives

  • @RalphDratman
    @RalphDratman 5 лет назад +6

    This is a wonderful presentation

  • @andrewdias2690
    @andrewdias2690 4 года назад +6

    This is a great lecture! I really like this approach to topology as opposed to other videos I've seen. And the way he mispronounces all these mathematicians' names is kinda adorable.

  • @definitelynotofficial7350
    @definitelynotofficial7350 3 года назад +4

    Is this guy part Greek or something? He said "γεωμετρία" (geometria) with perfect Greek accent and it really startled me because non-native speakers struggle with pronouncing words like it right, and he kinda looks Greek too.

    • @davidlozanocampillo2283
      @davidlozanocampillo2283 3 года назад +6

      He probably speaks Spanish well (mentioned that he was brought up in Mexico). Greek and Spanish phonetics are almost identical.

  • @kmd21886
    @kmd21886 Год назад +5

    ابدع بمعنى الكلمة

  • @Dglinski2
    @Dglinski2 5 лет назад +10

    I haven’t taken a college math course in about 5 years and even then didn’t get in to much conceptual math. What kinda prerequisites would someone need to know to understand topology? I’m very curious and this first lecture seemed fun even, I’ll attempt to keep following along but could anyone describe what fundamentals someone should know going in to this course that might make it easier to understand?

    • @aldogarcia6347
      @aldogarcia6347 4 года назад +9

      You will need algebraic and topological concepts. Good books in Algebra are Topic in Algebra by Herstein or Contemporary Abstract Algebra by Gallian. For topology, I can advise Munkers and Willard. Hope this helps.

    • @Jean-Berry
      @Jean-Berry 4 года назад +2

      Perhaps you should look up abstract algebra lectures by Benedict Gross here on youtube. They are also very fun! (sometimes could seem like its going way too fast tho)

    • @Jean-Berry
      @Jean-Berry 4 года назад +2

      Also, maybe you should also look up linear algebra, and for that I recommend lectures and book by Gilbert Strang on that subject. His lectures on linear algebra are lovely.

  • @SphereofTime
    @SphereofTime Год назад

    4:44 gauss bonet theorem

  • @tanmaymishra9576
    @tanmaymishra9576 7 месяцев назад

    until 21:00 , history of topology

  • @medhatrabie3071
    @medhatrabie3071 2 месяца назад

    I did not understand Poincare approach

  • @haneenballan7337
    @haneenballan7337 4 года назад +5

    Does anyone have a solution manual for the Allen Hatcher textbook?

  • @GEORGIOSMGEORGIADIS4
    @GEORGIOSMGEORGIADIS4 Год назад +3

    Here from Aleph 0's vid, wish me luck 🤞

  • @p_khale07
    @p_khale07 3 года назад +4

    what book did he mention when he said chapter 0,1,2 ?
    thanks in advance !

    • @bellfoozwell
      @bellfoozwell 3 года назад +6

      Allen Hatcher’s “algebraic topology “. Go to his website to get it.

    • @emanoelsouza8100
      @emanoelsouza8100 Год назад

      @@bellfoozwell thank you!

  • @dehnsurgeon
    @dehnsurgeon 2 года назад +2

    how did no one notice the typo at @53:06

    • @maazadnan117
      @maazadnan117 5 дней назад

      f to X, it means no one is getting what's goin on :D although no i'm satisfied that on the right track

  • @tcveatch
    @tcveatch Год назад

    Dumb question. How does the given definition of continuous (23:49) capture the meaning of “continuous”? Functions from an open domain to an open range have open BOUNDARIES (as in the open range (0,1) in contrast to the closed range [0,1]), but what continuity ACTUALLY means is continuous INSIDE the domain. A definition constraining the boundaries of set would not evidently constrain the interiors thereof. Maybe somebody could clarify, since the teacher didn’t. Thanks.

    • @gateronblackinksv2173
      @gateronblackinksv2173 Год назад

      I’m not exactly sure what you mean by “open boundaries”, but the intuition for this definition comes from analysis. In analysis, you can prove (from the epsilon - delta definition of continuity) that a function is continuous if and only if preimages of open sets are open sets. I believe Allen Hatcher also provides some intuition in his notes on point set topology, which you can find here: pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf

    • @tcveatch
      @tcveatch Год назад

      @@gateronblackinksv2173 edited question. Thank you!

  • @karimshariff7379
    @karimshariff7379 2 года назад +1

    What is the textbook he mentioned? Thanks.

  • @aous5880
    @aous5880 Год назад +1

    What are the mathematical requirements that I must study before I learn topology as a beginner, given that I did not study mathematics after high school

    • @pseudolullus
      @pseudolullus Год назад +2

      Set theory, proof writing, abstract algebra and point-set (standard) topology. This is a very advanced class, but also very enjoyable.

  • @ruijunlin4574
    @ruijunlin4574 4 года назад +3

    what is the lecture notes or textbook?

    • @BMK5298
      @BMK5298 Год назад +1

      Allan hatcher , algebraic topology

  • @randalllionelkharkrang4047
    @randalllionelkharkrang4047 Год назад

    do u know where we can find exercises/ book to accompany these lectures?

  • @tcveatch
    @tcveatch Год назад

    Another dumb question. At 32:30 he explains a “continuous family” of maps and writes F:Xx[0,1]->Y “so” (X,t) |-> f_t(X) is continuous. I find this uninterpretable, unreadable. 1) clearly f_t(X) is a map, since it is a function of X,that is, *maps* values of X to f_t(X). But in what if any sense is (X,t) a map; it is NOT a map, but rather a continuous open range of numbers from X to t. An open line segment is no map at all, more like a dead thing, a mere piece of space,the input to a map perhaps but not a map. 2) Does the scope of this particular F end after X or ] or Y? Y, I’ll guess, but then how can Y be the output if it’s part of the input? 3) Is the idea of a family that members map from one to another, so both the inputs and outputs are members of the family? If so Xx[0,1] must be a continuous map which it isn’t since it is a subregion of R^2. And Y must be a continuous map which it could be but not necessarily by anything written or said here. And (X,t) must be a continuous map which it isn’t since it is an open line segment. And f_t(X) must be a continuous map which it could be by assumption from Y being a continuous map but then we don’t really have reason to believe that yet, do we? So in what sense is this a family of continuous maps? Apparently none. 4) Maybe the map is BETWEEN things in Xx[0,1] and things in Y, and as an example (X,t) which is in Xx[0,1] seems to map according to what he said to f_t(X) which could only be an element in Y, if Y were some kind of universe of FUNCTIONS and f_t(X) an element in that universe, which I wish he would explain since I never heard of a domain or a range being a world of functions, since functions take domains to ranges, that would be a mixing and a confusion of categories, where I grew up. I mean, you could MENTION that Y is not a normal numerical range, some subset of R^n, but a “space” of functions or continuous maps or something, just you know, so I (we?) could understand you. I’ll have to wrap my head around that. Then what would make this map to a function in Y a continuous map, is something also evidently unstated. Is it the openness of the segment (X,t)? If so, that could be made explicit and then be explained, why that follows, too.
    Please help this struggling, concrete minded follower understand what you are saying.

    • @pavlosurzhenko4048
      @pavlosurzhenko4048 Год назад

      He wrote that the function acts like (x,t) |-> f_t(x) (x here is a small and represents a variable, not the space X), i.e. F is a function that maps Xx[0, 1] (with the product topology) into Y. Basically, you don't think of t as a parameter, but as another argument of the function F.
      The (x, t) |-> f_t(x) notation is the same as saying that F(x, t) = f_t(x).

  • @SphereofTime
    @SphereofTime Год назад

    6:42 riemman wants to go further

  • @farhanakausar4281
    @farhanakausar4281 2 года назад

    I want to show that Show O(p,q) is homotopic to O(p)×O(q) for p and q positive integers. Is there any hint or idea how to define homotopy?

  • @themathguy3149
    @themathguy3149 4 года назад +7

    God how can so much cool fit in one person?

  • @rhaldryn7511
    @rhaldryn7511 4 года назад +2

    What university is this?

  • @umergulzar4062
    @umergulzar4062 4 года назад

    I need help with some typical questions can u help

  • @Israel2.3.2
    @Israel2.3.2 5 лет назад

    Library doesn't have Hatcher. I like physical copies :(

    • @NotLegato
      @NotLegato 5 лет назад +2

      luckily hatcher is cheap as dirt. it's sub-30 pounds.

    • @Israel2.3.2
      @Israel2.3.2 5 лет назад +1

      @@NotLegato oh cool I'll order it then. Fascinating subject so far.

  • @Thehewhoviews
    @Thehewhoviews 4 года назад +1

    Timestamp 54:15

  • @isleofdeath
    @isleofdeath 3 года назад

    What book is the lecture using?

    • @feraudyh
      @feraudyh Год назад

      My impression is that he is referring to the book Algebraic Topology by Allen Hatcher, even though he mentions it as Patrick's book.

  • @hassaannaeem4374
    @hassaannaeem4374 2 года назад

    great!

  • @jmxu0405
    @jmxu0405 5 лет назад +5

    I couldn't help mistake him for Jimmy Carr

  • @1995amittai1
    @1995amittai1 3 года назад +1

    The algebraic topology Feynman

  • @98danielray
    @98danielray 4 года назад

    7:00
    what gives the "locally resembles a plane" characteristic is curvature, not homeomorphism to planes. otherwise, thanks for the great lecture

    • @arismartinian3346
      @arismartinian3346 4 года назад +9

      I know this is an old comment, but I'm not totally sure what you mean. An n-dimensional manifold is defined by its having a neighborhood around an arbitrary point homeomorphic to Euclidean n-space. Curvature is only defined on certain smooth manifolds.

  • @suup4k75
    @suup4k75 Год назад

    I wonder where he learned to pronounce poincare this way

  • @samspeight4944
    @samspeight4944 3 года назад

    The answer is always no if you use infinity-categories ;)

  • @Gangstabob716
    @Gangstabob716 Год назад +1

    This is one of the easiest classes I took at my university. I don't understand how people struggle with this subject

  • @maciej12345678
    @maciej12345678 2 года назад

    11:47 this is nonsens what he saying -- saying first something else then something different and then that that answer to other question but to first is NO very twisted why to say something and try not say what realy neeed to say-- but still something new

  • @MoonBull13
    @MoonBull13 2 года назад

    Why do they still use chalk boards. I cringe and get goosebumps hearing chalk or erasers on them

  • @probablyshadman
    @probablyshadman 2 года назад

    I'm from all over the place 😆

  • @krakenmetzger
    @krakenmetzger 5 лет назад +11

    Please buy a better eraser

  • @dfs6575
    @dfs6575 Год назад

    I don’t think organic chemistry tutor will save me this time

  • @testchannel-pg5vd
    @testchannel-pg5vd Год назад

    I am from all over place

  • @johnstfleur3987
    @johnstfleur3987 Год назад

    "17."

  • @xerxes1871
    @xerxes1871 3 года назад

    So many holes to fill in......

  • @johnstfleur3987
    @johnstfleur3987 Год назад

    "STEVE JOBS IS ALIVE."(AYANA)

  • @TheDavidlloydjones
    @TheDavidlloydjones 6 месяцев назад

    The backs of people's heads as the write n blackboards are not a fit subject for RUclips. It's been done already. Two of them was too many.
    If you want to teach a class, teach a class.
    If you want to make a video, sure, make a video.
    Just try to get it straight in your head that they are two different things, OK?

  • @hamzehabuabed6333
    @hamzehabuabed6333 4 года назад

    Why you are laughing

  • @fslakoh
    @fslakoh Год назад

    Math is Nice but totaly unuseful Profs are paid juste for fun 🎉

  • @rookitchen
    @rookitchen 4 года назад +2

    laughing should not be allowed in a math class. This should be a fundamental axiom of all math classes.

    • @UnderscoreZeroLP
      @UnderscoreZeroLP 4 года назад +2

      not funny

    • @beback_
      @beback_ 4 года назад +16

      Not allowing things should not be allowed in a math class.