The universality of Hom complexes

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It is shown that if T is a connected nontrivial graph and X is an arbitrary finite simplicial complex, then there is a graph G such that the complex Hom(T,G) is homotopy equivalent to X. The proof is constructive, and uses a nerve lemma. Along the way several results regarding Hom complexes, exponentials, and subdivision are established that may be of independent interest.
14 pages, 12 figures

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Combinatorics, Algebraic Topology, 05C15, 55P15, 57M15

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http://salesiana.dossiersoluciones.com/handle/123456789/124129

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702471
 http://arxiv.org/abs/math/0702471

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arXiv