## The Stiefel-Whitney Characteristic Classes

### Zachary Johnston – Clemson University

The Stiefel-Whitney characteristic classes of a real vector bundle with base space B are a sequence of cohomology classes of B over Z/2Z. Consequently, they are used as an algebraic invariant for distinguishing topological spaces and real vector bundles. More surprisingly, they provide an obstruction to a topological space being the boundary of a smooth compact manifold, given by the cobordism theorem. The Stiefel-Whitney characteristic classes also allow one to conclude some unexpected results classifying which projective spaces can be parallelizable and which can be immersed into a fixed Euclidean space.