Algebraic topology: Introduction

This lecture is part of an online course on algebraic topology.

This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism).

[insising]

Let's goooo! This is going to be epic!

[Helmutandmoshe]

I am sure hoping that you will continue this series on Algebraic Topology. What a great gift these teachings are to the mathematical community... and eventually, through secondary contacts and so on, the rest of the world. Thank you.

[simplicjusz]

The other day, I learnt combinatorics from Prof. Gowers, now, I am listening to Prof. Borcherds on algebraic topology. Who needs universities? Long live the lockdown!

[Jop_pop]

This is incredibly perfect - was literally just looking for a course in algebraic topology and found Hatcher's book! Then this comes out the same day??

[LernRead]

Thanks Dr. Borcherds, very timely as well - I had just begun reading a bit more about algebraic topology and was hopelessly lost. Will look forward to more videos soon.

[codatheseus]

THANK YOU!! Ive spent years trying to understand a handful of things that just kept eluding me about complex functions and this lecture cleared them up!

[melanthajezek]

The lack of notification of your videos has been eating me up for days. I'm so relieved you uploaded! I got too used to these daily videos. I understand you must be working on something amazing right now hence the gaps. Good luck and thank you!

[robertschlesinger]

Excellent lecture. Very interesting, informative and worthwhile video. Many thanks.

[ConradMorris-lh]

Thank you for providing this content and giving back to the mathematical community. 😊

[dontwannabefound]

Incredible Prof Borcherds, I should have taken some of your classes while I was at Berkeley!

[CAL-]

This information is very helpful and valuable. Thank you!

[Barbapippo]

Thanks! I look forward to the next lectures, :)

[mrpotatohed]

been wanting a supplement for this topic, looking forward to more, thank you.

[빵빵빵-mo]

I remember hearing about fundamental groups and such at topology2 class. The teacher was kind and good.

[vijaykumarsharma]

Exciting ! We do it for the fun of it 🤘🏻 Thanks professor 😊

[f-th]

I remember reading that the first homology group is the Abelianization of the fundamental group. (someone please correct me)

[harisserdarevic]

Thank you for uploading this lecture! I'm currently a 3rd year undergraduate math student, what would be a good prerequisite for this class? I have strong experience in abstract algebra but not much topology background

[MagicBoterham]

What's R/Z, real numbers with the integers removed?

[hannesstark]

I missed it. So glad the videos are back and better than ever!

[pmcate]

What is the difference between Z and the free group on a, b? It seems like they should be isomorphic since Z also has two generators.