Introduction to Homological Algebra III: Higher Dimensional Examples

In this lecture, I introduce a few basic “higher dimensional examples” of chain complexes.

[Drachensslay]

7:33 is really neat! Fantastic visual and the coloring is so intuitive!

[moygil]

Thank you very much, very clear and intuitive, any chance you to see more videos from you on this topic or something on homotopy theory or algebraic geometry?

[InfiniteQuest]

Nice videos! I actually found this trying to study TDA. I have a bunch of Algebraic Topology/Topology/Homology GTM books, but sheesh they are dense. This is really helpful and concrete. Too many textbooks just live in abstraction. Sure you can prove theorems, but how the heck to do you apply it to anything?!

[alial]

Awesome. Thx . Why did you stop doing such great lectures?

[tian]

Is there any chance I could see how you solve for the master equation as you did at 5:05 but with the triangle and sphere? I'm unsure whether the boundary of the triangle edges are equal

[daigakunobaku]

This loops looks wrong, and the orientation lines on sigma look wrong. A consistent orientation would imply that gamma_{0} and gamma_{1} are both oriented counter-clockwise or both oriented clockwise. How does this work? The 2-simplex example looks even more wrong, the boundary operator should give [12], [23], [31], not [12], [23], [13].

[dbp_patel_]

Lovely! Which app do you use for these "handwritten" slides?

[Relative]

I don't see how, you decide the directions of the arrows in the various complexes, sure if you switch a direction you flip a + to a - but how do you decide where to start?

[MikhailBarabanovA]

It has some infinity category feel. Is this somehow related?