MAI0126 Topological combinatorics
- Lecture plan
Here is a tentative plan of the lectures. It will be continuously
updated. Unless otherwise noted, the time is 13:15–15:00 and the
venue is Kompakta rummet.
Date We did/plan to do: Sep 4 Versions of the Borsuk-Ulam theorem. Simplicial complexes. Sep 11 Tucker's lemma. Simplicial homology. Sep 17 Finish proof of Tucker's lemma. Lyusternik-Shnirel'man's version of Borsuk-Ulam. The Kneser-Lovász theorem. Sep 25 Box complexes and the Z_2 index Oct 9 Neighbourhood complexes. Connectivity bounds for chromatic numbers. Oct 16 Proof of the connectivity bounds from last time Oct 23 Introduction to Part 2. Collapsibility. Oct 30 More on matchings. Proof of the Closure Theorem. Evasiveness. Nov 6 Cell complexes. Elements of discrete Morse theory. Nov 13 Something about cellular homology. Shellability. Nov 20 Lexicographic shellability Nov 27 Quillen's fiber theorem. Nerve lemmas. Crosscuts.
Sidansvarig: axel.hultman@liu.se
Senast uppdaterad: 2019-11-29