The universality of Hom complexes

Details The universality of Hom complexes The universality of Hom complexes

2007-02-16

arxiv.org/abs/math/0702471v1

Mathematics

Combinatorics

14 pages, 12 figures

Scientific paper

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.

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