Pattern-equivariant cohomology with integer coefficients

Equivariant Cohomology with Local Coefficients

We show that for a discrete group G, the equivariant cohomology of a G-space X with G-local coefficients M is isomorphic to the Bredon-Iliman cohomology of X with equivariant local coefficients M.

Pattern Equivariant Functions and Cohomology

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier accessible. It is based on generalizing the notion of equivariance from lattices to point patterns of finite local complexity.

Equivariant Simplicial Cohomology With Local Coefficients and its Classification

We introduce equivariant twisted cohomology of a simplicial set equipped with simplicial action of a discrete group and prove that for suitable twisting function induced from a given equivariant local coefficients, the simplicial version of Bredon-Illman cohomology with local coefficients is isomorphic to equivariant twisted cohomology. The main aim of this paper is to prove a classification th...

The equivariant spectral sequence and cohomology with local coefficients

In his pioneering work from the late 1940s, J.H.C. Whitehead established the category of CW-complexes as the natural framework for much of homotopy theory. A key role in this theory is played by the cellular chain complex of the universal cover of a connected CW-complex, which in turn is tightly connected to (co-)homology with local coefficients. In [8], we revisit these classical topics, drawi...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology