Math 282B - Intro to Homotopy Theory - Spring 2017


Class times and Location: Tue, Thu 1:30pm - 2:50pm at Building 240, Rm 110
Instructor: Nathan Perlmutter
Office: 384-D
Office hours: TBA

Topics: Homotopy groups, CW complexes, fibrations, Eilenberg-MacLane spaces, simplicial sets and spaces, homotopy limits and colimits, spectral sequences.

Prerequisites: Math 215A or similar. Some differential topology could be helpful.

Books: Most of what I cover will be from "Algebraic Topology" by Hatcher, "Spectral Sequences in Algebraic Topology" also by Hatcher (this is an unpublished book free on Allen Hatcher's website). I also plan to draw material from "Lecture Notes in Algebraic Topology" by Jim Davis and Paul Kirk.

Lecture plan.
4/4 Homotopy groups, relative homotopy groups, exact sequence of a pair.
4/6 Weak homotopy equivalences, whitehead's theorem. Begin excision for homotopy groups, Freudenthal suspension theorem.
4/11 Hurewicz theorem. Begin fibrebundles and fibrations.

Date Link to exercise sheet
4/27 Homework 1
5/25 Homework 2