2011 USTC GEOMETRY SUMMER SCHOOL

LOCATION: UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA, HEFEI, CHINA

COURSE: ALGEBRAIC TOPOLOGY

office:

e-mail:

CLASS SCHEDULE: Tu, Thu, Sat 14:30-17:00, Room 5406.

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

DESCRIPTION: Higher homotopy groups, fibrations, spectral sequences, bundle theory, classifying spaces, vector bundles, characteristic classes, applications and calculations.

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

HOMEWORK: it will be assigned weekly and will be discussed in class with student participation.

HW 1: Homotopy theory (due June 7, 2011)
HW 2: Spectral Sequences (to be discussed in class on July 12, 2011)
HW 3: Characteristic classes (to be discussed in class on July 14, 2011)