Combinatorical Algebraic Topology

Class Info Class Number: Math 407-001 Dates: Sept 4 2012 - Dec 6 2012 + final Room: NS 319 Meeting time: Tues/Thurs 5B-6B (1:30 - 2:50) Text: Jiří Matoušek's 'Using the Borsuk-Ulam Theorem' Prof: Mark Siggers Office Hours

Links Class Infomation

Syllabus

We will cover as much as we can of the beautiful text `Using the Borsuk-Ulam Theorem' by Jiří Matoušek, in which a streamlined treatment of combinatorial algebraic topology is used in several important combinatorial and geometric applications.

We start by introducing simplicial complexes and discuss homotopy theory as it applies to them (Chap 1). With only minimal consideration of topological ideas, we prove the Borsuk-Ulam and related Theorems, and use them in important combinatorial applications such Lovasz-Knesser Theorem (Chap 2-3).

Delving deeper into algebraic topology, using many ideas of (though largely avoiding the notation of) homology and cohomology, we look at the (more) original proof of the Lovasz-Knesser theorem, and extensions of it.

Homework.

There will be weekly homework problems to hand in. Occasionally (once or twice during the semester) you will be asked to present a solution to the class.

Tests

There will be two tests. The first one will be ??, and the final will be ??. We will decide the date of the exams at least 2 weeks before the exam.

Evaluation

HW: 10%, Presentation: 10% . Tests 2 x 40%. For the HW mark, we will have 8 - 10 assignments, and I will drop the bottom two. Only the bottom two, so this is an attendance mark as well.