18.906: Algebraic Topology II
Monday, Wednesday, 11:00-12:30, 2-139
Subject matter: Basic homotopy theory, obstruction theory, classifying spaces, spectral sequences, characteristic classes.
Final exam: There will not be one.
Homework: Due fortnightly. Likely due dates: Mondays Feb 25, Mar 11, Apr 1, Apr 17 (Wednesday), May 6, May 15 (Wednesday).
Office hours: Monday, Wednesday 1:00-2:00, or by appointment.
- PS1, due Feb 25
- PS2, due Mar 11
- PS3, due Apr 1
- PS4, due Apr 17
- PS5, due May 6 (fixed typo in P.6)
- PS6, due May 15 (fixed typos in P.3, P.6)
A Concise Course in Algebraic Topology.
John Milnor and James Stasheff,
Robert Switzer, Algebraic Topology.
Paul Goerss and Rick Jardine, Simplicial Homotopy Theory.
Charles Weibel, Introduction to Homological Algebra
- For a careful treatment of compactly generated weak Hausdorff spaces, you may wish to look at Neil Strickland's notes.
- For a very systematic treatment of cofibrations and fibrations, consider Hirschhorn.
- For a proof of the local nature of fibrations, see [May, Section 7.4].
- For a nice treatment of principal bundles from the simplicial point of view, consider [Goerss-Jardine, Sections V.3 and V.4].
- For the construction of the spectral sequence of a filtered complex, see for example [Weibel, Sections 5.4 and 5.5].