Abstract: The Borsuk-Ulam Theorem is one of the most famous theorems of algebraic topology. After stating it and a couple of equivalent versions, we shall discuss some of its history and applications. Then we show how it can be generalized - instead of starting with a sphere and the antipodal involution we can consider any finite dimensional CW-complex X and a fixed point free involution on X. The results obtained represent joint work with Claude Hayat (Toulouse) and Daciberg Lima Goncalves (Sao Paulo), and we shall show how they lead to a complete solution of the problem when X is a manifold of dimension 2 or 3.

This talk will be accessible to graduate students.