What is algebraic topology?

An introduction to homology, a key concept in algebraic topology. Take your personal data back with Incogni! Use code ALEPH at the link below and get 60% off an annual plan: http://incogni.com/aleph.

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This video is a collaboration with Trevor from the channel Mathemaniac. Check out his video here:    • The "textbook exercise" on Euler char...  .

A HUGE thank you to Brendan Shuttleworth for working with me to make the script and storyboard for this video. You rock Brendan!

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SOURCES and REFERENCES for Further Reading:

This video is a quick-and-dirty introduction to homology. But as with any quick introduction, there are details that I gloss over for the sake of brevity. To learn these details rigorously, I've listed a few resources down below.

(a) Video Lectures by Pierre Albin:    • Algebraic Topology - Pierre Albin  

(b) “Algebraic Topology” by Allen Hatcher: https://pi.math.cornell.edu/~hatcher/...

CORRECTIONS:
12:59 You take n-cycles/(n+1)-boundaries not n-chains.

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MUSIC CREDITS:

The song is “Taking Flight”, by Vince Rubinetti.
https://www.vincentrubinetti.com/

00:00-1:11 Intro
1:11-2:15 The Overall Idea
2:25-4:25 Cells
4:25-6:15 The Circle
6:15-7:00 Sponsored Message
7:00-8:55 The Torus
8:55-11:10 Homology, in general
11:10-14:37 Singular Homology