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