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Cohomology of colorings of cycles

Dmitry N. Kozlov
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Abstract

We compute the cohomology groups of the spaces of colorings of cycles, i.e., of the prodsimplicial complexes Hom(C_m,K_n). We perform the computation first with Z_2, 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(C_m,C_n) onto a garland of cubes.

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Dmitry N. Kozlov. 2006-04-13. Cohomology of colorings of cycles. https://arxiv.org/abs/math/0507117

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