Video

what is the textbook for this course?

This may seem like completely useless math, but Homology could be used to generate structural models of proteins, for instance.

59:08 i like this map ! Cute trick for insuring tangence to the sphere, and nice "Complex looking" 2-block rotations 👌 almost disappointing that there is no sneaky way to search for odd spheres 😂

im thinking the theorem indicates a bijection from coset to p^-1(x0) would not work for the left cosets since that subgroup isnt normal

A good pair of lectures.

The backs of people's heads as the write n blackboards are not a fit subject for CZcams. 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?

Ew why is that chalkboard brown?

until 21:00 , history of topology

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

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.

I got it. Really rather well explained. But I probably could'nt do the homework.

Good Morning !

these lectures explain Alan Hatchers book really well

Girl at 45:19 is GORGEOUS

Three cups of coffee and he’s good lol

Math profs only regurgitate text book material while writing it on the blackboard. They present no insights that are not available in the text book. For instance they never give examples using real physical integers for functions or fields that would help explain abstract concepts. Their excuse for this abominable dereliction of duty. "If you need examples you don't belong here." LOL

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.

This man is a good lecturer

E≡MC²³

Bary weight or Barry white?

00:31:32 the book is Algebra and Galois theories by Adrien Douady, who was a mathematician of Grothendieck's caliber, and is behind a great deal of major mathematical results of the XXth century. You dont hear about him because his name does not appear in the articles, but he is behind a lot of Serre's results, Wiles, Yoccoz, Atiyah, Connes, Weil and Grothendieck... He had a nack for visualizing the steps conducting to the proofs of several conjectures, sharing his ideas without proving them. He has major results of his own in Complex Dynamics.

homotopy

i remember my teacher back in 2003-2004 on algebra in Iasi , Romania , big idiot i was cause i reject everything , i was easy an 8 out of 10 marks without any eforts but later i discover nightlife vodka and beers and all my life changes! mental health matters

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

I'm a bit confused by the definition of a good pair. Is there a closed subspace A of X (topological space) that is not a deformation retract of a neighborhood in X? The definition suggests that the answer is yes but I don't see how this is possible.

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

Arara

I wonder where he learned to pronounce poincare this way

Page 94 barrister = n 1 Also called: barrister-at-law. (in England) a lawyer who has been called to the bar and is qualified to plead in the higher courts. Cf. solicitor. 2 (in Canada) a lawyer who pleads in court 3 US. a less common word for lawyer. [C16: from BAR'] Barry is a male name.

This is obviously too late for a comment like "hey, cameraman, don't follow the lector, follow the BOARD instead", but just in case no conclusion was made, here it is.

you know how hard it is when the musical symbols start appearing

4:44 gauss bonet theorem

6:42 riemman wants to go further

Grateful for the lectures, but this one (No. 15) is absolutely horrible in video quality. Unfortunate, since it is about one of the more technical proofs of the whole course.

What does it mean to calculate a group?

Filmed from an angle which makes it difficult to see the writing clearly.

Starfish do not have tentacles, they have arms.

This is Mat Neth's net math.

I think he was writing path products (path concatenation) backwards when proving the conjugacy of the subgroups induced by different basepoints. It is standard to write a path product from left to right. We should write: p2_*([gamma^-1 • a • gamma]) = [a^-1 • b^-1 • a • b • a] = p2_*([gamma])^-1 • [a] • p1_*([gamma]), where [f] |-> [gamma^-1 • f • gamma] is the isomorphism from pi_1(X~, x~_1) to pi_1(X~, x~_2) along the path gamma. In general, the map: [g] |-> [b • a]^-1 • [g] • [b • a] for all [g] in pi_1(X, x) is an inner automorphism taking H_1 to H _2.

The “topologist’s sine curve” is semi-locally simply connected but not locally simply connected (nor is it locally path-connected). Consider an open ball around a point within the space on the y-axis. This neighborhood is not path-connected, but any loop within the neighborhood is entirely contained either on the y-axis or in the “curvy” part of the space with positive x-coordinates, and any such loop is null-homotopic.

1:08:55 This should say “y’ in f^-1(U)”, where this is an open subset of Y.

I like this proof of the fun theorem of algebra.

I am from all over place

37:10

I think that the confusion at the beggining was caused because freedom of the action ρ is equivalent to injectiveness of the shear map, s:G×Y->Y×Y defined by s(g,y)=(gy,y).

Relation between homotopy of maps between two.spaces and homotopy equivalence? h is a path traced by image of base point induced homomorphism given by composed with the given map

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.

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.

Best course in algebraic topology so far

Does path connected not imply locally path connected? In the general lifting criterion, both of these things are assumed, but I thought path connected implies locally path connected.