Generalizing a result of Depauw, we prove that the geometric cohomology groups for a Z d action are in any dimension isomorphic to the Feldman-Moore cohomology groups rsp. the algebraic group cohomology groups. This result holds in the smooth, topological or measurable category and for general Polish groups as coeecient groups.

In this paper a fast algorithm to compute cohomology group generators of cellular decomposition of any orientable closed 2-manifold is presented. The presented algorithm is a dual version of algorithm to compute homology generators presented by David Eppstein [12] and developed by Jeff Erickson and Kim Whittlesey [13]. Keyworks computational cohomology, cohomology generators, combinatorial 2-ma...

A discrete group G has periodic cohomology over R if there is an element in a cohomology group, cup product with which induces an isomorphism in cohomology after a certain dimension. Adem and Smith showed if R = Z, then this condition is equivalent to the existence of a finite dimensional free-G-CWcomplex homotopy equivalent to a sphere. It has been conjectured by Olympia Talelli, that if G is ...

Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of the weighted projective spaces, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan, toric varieties, the localization technique) which have been proved t...