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arXiv · 1202.1872

Every finite complex has the homology of some CAT(0) cubical duality group

Raeyong Kim
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Abstract

We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally $\mathrm{CAT}(0)$ cubical complex $T_{X}$ and an acyclic map $t_{X} : T_{X} \to X$ such that $π_1(T_X)$ is a duality group.

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Raeyong Kim. 2012-12-10. Every finite complex has the homology of some CAT(0) cubical duality group. https://arxiv.org/abs/1202.1872

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