What is...relative homology?
Goal. Explaining basic concepts of algebraic topology in an intuitive way. This time. What is...relative homology? Or: Calculations modulo subspaces. 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. http://www.dtubbenhauer.com/youtube.html Website with exercises. http://www.dtubbenhauer.com/lecture-a... Relative homology. https://en.wikipedia.org/wiki/Relativ... https://math.stackexchange.com/questi... https://ncatlab.org/nlab/show/relativ... Short and long exact sequences. https://en.wikipedia.org/wiki/Exact_s... Pictures used. https://slideplayer.com/slide/11382479/ https://en.wikipedia.org/wiki/Exact_s... Hatcher’s book (I sometimes steal some pictures from there). https://pi.math.cornell.edu/~hatcher/... Always useful. https://en.wikipedia.org/wiki/Counter... Mathematica. #algebraictopology #topology #mathematics

What is...a (co)homology theory?

An introduction to homology | Algebraic Topology 30 | NJ Wildberger

What is...cohomology?

Algebraic Topology 12: Intro to Singular Homology

18 Relative homology as absolute homology

What is a Hilbert Space?

What is algebraic topology?

13. Homotopy Invariance of Homology; Exact Sequences - Pierre Albin

Introduction to Persistent Homology

The Dirichlet Integral is destroyed by Feynman's Trick

Relative Homology 1

When Math Isn’t Based in Reality

Algebraic Topology 15: Exact Sequence of Homology and Excision

What is...homology intuitively?

Simplicial Complexes - Your Brain as Math Part 2 | Infinite Series

Computing homology groups | Algebraic Topology 33 | NJ Wildberger

The 7 Millenium Problems Explained In 7 Minutes

What is...the Hodge conjecture?

16. Equivalence of Simplicial and Singular Homology - Pierre Albin

