What is...algebraic topology?

Goal.
Explaining basic concepts of algebraic topology in an intuitive way.

This time.
What is...algebraic topology? Or: Translating from topology to algebra.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Disclaimer.
These videos are concerned with algebraic topology, and not general topology. (These two are not to be confused.) I assume that you know bits and pieces about general topology, but not too much, I hope.

Slides.

Website with exercises.

Material used.

The four main fields (I also stole some pictures from there).

Awesome fundamental group animations (and other great stuff).

Fundamental group.

Fundamental theorem of algebra using pi_1 (I also stole some pictures from there).

Topological data analysis.

Venn diagrams in latex.

Hatcher’s book (I sometimes steal some pictures from there).

Always useful.

#algebraictopology
#topology
#mathematics

[lacusrengoku]

thank you for taking the effort to make these very intuitive slides. I have been trying to study abstract topology myself....had some engineering math background (e.g., real analysis and differential geometry).... but still struggling with this topic. Your videos helped!

[francescabeard]

You've inspired my daughter to look into studying topology at university - we thoroughly enjoyed your video!

[apokryphos_]

Your videos are extraordinarily helpful building intuition and really helped me along my AT studies. By pure accident I today stumbled over the fact that you very well know my lecturer and bachelor thesis mentor, Prof. Dr. Thomas Schick :D Greetings from Göttingen and keep up the amazing work!!

[JackLee-dphm]

Please continue to update this series. I am studying AT and your videos truly give me a good understanding of AT and some interesting ideas.

[HDQuote]

Thanks for the video! Wow, I would have never thought that there would be such a close connection between topology and data analysis. This really motivates me to look closer into it

[NoNTrvaL]

Absolutely amazing playlist and channel!

[valentinussofa]

This lecture enrich my insight about algebraic topology with visualization. Thank you very much🙏

[yamansanghavi]

Your videos are extremely helpful. I can't thank you enough.

[mohitdas]

ur videos are amazing and enlightening . Please do something on differential topology also in intuitive and visual way

[speedbird]

Very nice introduction,
Good tutorial,
I really enjoyed it,
Thanks!

[jijuanzheng]

I hope you have a video explain fiber bundle I could not find it, I am also interested in why we need it and how it is useful with use cases, thx

[shadowlord]

Amazing playlist that I discovered today.I have studied only upto homology.Can you suggest good book for cohomology groups?

[Englandcricket]

Hey Sir. Asking something we asked today as Mathematics Student. Why Topology is Called Abstract Branch of Mathematics? Kindly explain

[tayzrayz]

Very excellent explanation, never fails also r u russian