**Department of Mathematics**

TOPOLOGY SEMINAR

"A theorem of Carlsson on finite free G-complexes"

Abstract:If G=(Z/2)^r acts freely and cellularly on a finite CW-complex X, then the homology of X satisfies an inequality involving the structure of H_*(X; Z/2) as a Z/2[G]-module. In the case where the induced action on homology is trivial, this inequality gives that if G=(Z/2)^r acts freely on a finite complex X, then X must have at least r+1 non-vanishing homology groups. This inequality is proved by Carlsson and using this, he concludes that if G=(Z/2)^r acts freely on X=(S^n)^k with trivial action on homology, then r is less than or equal to k. In this talk, I will give the proof of this theorem. The proof uses the method of converting the problem in commutative algebra related to DGA’s over a polynomial ring.

**Date: ****Monday, October 24, 2016**

**Time: ****13.40-14.30**

**Place: ****Mathematics Seminar Room,
SA-141**

**All are most cordially invited.
Tea and cookies will be served after the talk.**