# Equivariant cohomology of (Z_2)^r - manifolds and syzygies

Research paper by Volker Puppe

Indexed on: 30 Dec '15Published on: 30 Dec '15Published in: Mathematics - Algebraic Topology

#### Abstract

We consider closed manifolds, which occur as intersections of products of spheres of the same dimension with certain hyperplanes. Among those are the so called (big) polygon- and chain spaces. The equivariant cohomology with respect to natural actions of 2-tori is calculated and related to the notion of syzygy. It turns out that the equivariant cohomology module of these manifolds is often torsion free, but not free over the cohomology of the group. Coefficients are taken in the field with two elements.