Cohomology of colorings of cycles
Abstract
We compute the cohomology groups of the spaces of colorings of cycles, i.e., of the prodsimplicial complexes Hom(Cm,Kn). We perform the computation first with Z2, and then with integer coefficients. The main technical tool is to use spectral sequences in conjunction with a detailed combinatorial analysis of a family of cubical complexes, which we call torus front complexes. As an application of our method, we demonstrate how to collapse each connected component of Hom(Cm,Cn) onto a garland of cubes.
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