Math 581DA and 582DA
Characteristic Classes
and Cobordism
Ethan Devinatz
Autumn 2003 and Winter 2004, Monday-Wednesday-Friday 11:30-12:20
Topics include vector bundles, general fiber bundles, classifying spaces,
Stiefel-Whitney and Chern Classes with applications to immersions of
manifolds and the existence of linearly independent vector fields on
manifolds. The main goal of the sequence will be the computation of the
unoriented smooth cobordism ring and the proof that a smooth closed
manifold is a boundary (of a smooth compact manifold) if and only if all of
its Stiefel-Whitney numbers are 0. This will require development of the
Steenrod algebra and some tools from homotopy theory.
Prerequisites: A first year course in algebraic topology (such as
564-5).