# MATH 848X: Homotopy Theory and Characteristic Classes,
Spring 2018

## Professor Jonathan Rosenberg

This course will be an introduction to homotopy theory
and characteristic classes, focusing on those aspects of the subject
most needed to for work in geometry and topology (of all sorts),
geometric analysis, and algebraic geometry. All of these subjects
depend on this material to a greater or lesser extent, and it is
not taught in our regular first-year courses.

The course will pretty much take off where MATH 734 finishes off
(i.e., cohomology groups, cup products, and duality on manifolds).
Thus MATH 734 is the basic prerequisite, though students who have
done well in MATH 730 should be able to follow everything if they
are willing to fill in a bit on cohomology on their own.

There will be no assigned textbook
to purchase. Good free introductions
to the subject are available in Peter May's
A Concise Course in Algebraic Topology and Allen Hatcher's
Algebraic
Topology, Ch. 4 and his supplements
on Spectral
Sequences and
Vector Bundles.

For the syllabus the last time the course was given,
click here, though I will probably
change the approach to some of the topics in light of more recent
trends in homotopy theory.