Koszul duality and equivariant cohomology for tori
- Prelegent(ci)
- Matthias Franz
- Afiliacja
- Uniwersytet Grenoble 1, Francja
- Termin
- 15 kwietnia 2003 14:30
- Informacje na temat wydarzenia
- 5081
- Seminarium
- Seminarium „Topologia algebraiczna”
Koszul duality (in its simplest form) refers to the equivalence of derived
categories of differential modules over symmetric and exterior algebras.
Goresky, Kottwitz, and MacPherson have shown that one can use Koszul duality
to compute the real equivariant cohomology of a $G$-space as $H^*(BG)$-module
from the non-equivariant cochain complex. Similarly, the equivariant cochain
complex determines the ordinary cohomology as $H_*(G)$-module.
For the case of torus actions and singular cohomology, I will present
a different approach which extends to arbitrary coefficients. It permits
moreover to recover the product structure in equivariant cohomology.
As application I will describe the integral cohomology of smooth toric
varieties. This complements a result of Buchstaber and Panov.