Department of Mathematics
"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 DGAs over a polynomial ring.
Date: Monday, October 24, 2016
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.
Tea and cookies will be served after the talk.