ALGEBRAIC TOPOLOGY II.

office: 713 Van Vleck
e-mail: maxim@math.wisc.edu
office hours: TuTh 11-12

CLASS SCHEDULE: TuTh 9:30AM-10:45AM, Room B135 Van Vleck.

CLASS HOMEPAGE: http://www.math.wisc.edu/~maxim/754s18.html

DESCRIPTION:

1. higher homotopy groups, elements of obstruction theory, fibrations,
2. spectral sequences, applications (homology of groups, homology of covering spaces, homotopy groups of spheres),
3. bundle theory, classifying spaces, applications to manifolds,
4. vector bundles, characteristic classes, cobordism, and various applications.

READING SOURCES:

• Allen Hatcher: Algebraic Topology, available here.
• Allen Hatcher: Spectral Sequences in Algebraic Topology, available here.
• James Davis, Paul Kirk: Lecture Notes in Algebraic Topology
• John Milnor, Jim Stasheff: Characteristic Classes

GRADE:

Based on homework and participation in class.
As part of class participation, each student is expected to type up a week worth of lecture notes.

LECTURE NOTES: (to be updated regularly)

• Notes on homotopy theory
• Notes on spectral sequences and applications
• Notes on bundle theory
• Notes on characteristic classes and applications