## Topology Seminar: Marc Stephan

- Date: 06/05/2019
- Time: 15:00

University of British Columbia

A multiplicative spectral sequence for free p-group actions

Carlsson conjectured that if a finite CW complex admits a free action by an elementary abelian p-group G of rank n, then the sum of its mod-p Betti numbers is at least 2^n. In 2017, Iyengar and Walker constructed equivariant chain complexes that are counterexamples to an algebraic version of this conjecture. Their work raised the question if these chain complexes can be realized topologically by free G-spaces to produce counterexamples to Carlsson’s conjecture. In this talk, I will explain multiplicative properties of the spectral sequence obtained by filtering the mod-p cochains of a space with a free p-group action by powers of the augmentation ideal and deduce that the counterexamples can not be realized topologically. This is joint work with Henrik Rüping.

Location: ESB 4133 (PIMS Lounge)