Abstract: Let F_2 denote the field with two elements and let W, V be vector spaces over F_2. A quadratic map Q:W--> V is a function such that B(x,y)=Q(x+y)+Q(x)+Q(y) is bilinear. Quadratic maps are natural generalization of quadratic forms where the classification problem has been solved by Cahit Arf via what is now known as Arf invariant. In this talk, I will first give some examples of quadratic maps from homotopy theory, 2-group theory, modular representation theory, and restricted lie algebra theory. Then, I will present some recent results (joint with Jon Pakianathan) on Bockstein closed quadratic maps, and give some applications of our results to cohomology of groups.

Ergun Yalcin

General Seminar, 18.12.2003