Instructor: Sasha Voronov
10:10-11:00 MWF, VinH 311
Prerequisite: Math 8301 or basic knowledge of homology or cohomology,
the fundamental group, and manifolds
Textbook: Allen Hatcher. Algebraic Topology. Cambridge University Press,
Cambridge, 2002. $34.10 paperback. Also available on line at
http://www.math.cornell.edu/~hatcher/#ATI
Description: The goal of the one-year course is to study the powerful machinery of algebraic topology and provide necessary background for a student planning to work in the fields of algebraic topology, algebraic geometry, geometric topology, symplectic geometry, K-theory, algebra, gauge theory, mathematical physics, etc. The course may be considered an independent course in algebraic topology covering complementary topics to those studied in Math 8301-8302: Manifolds and Topology. However, the full mastery of Math 8301-8302 is not required: you just need to know some basics of homology theory and the fundamental group. We plan to study the following basic topics: homology and cohomology theories (including axiomatic, cellular, and singular homology, the Künneth theorem, universal coefficient theorems, cup products, and Poincaré duality), homotopy theory (including fibrations and cofibrations, homotopy groups, long exact homotopy sequences, the Whitehead and Hurewicz theorems, Eilenberg-Mac Lane spaces, etc.). We will also study a selection of topics, depending on time and interest. These topics may include Postnikov towers, cohomology operations, vector bundles, classifying spaces, characteristic classes, K-theory, cobordisms, etc.
Requirements: There will be homework throughout the year, but no exams. One in-class topic presentation in the second semester will be expected.
More information: Contact the instructor at
voronov@umn.edu
VinH 324
624-0355