Highly Influenced

# The Universality of Hom Complexes

@inproceedings{Dochtermann2007TheUO, title={The Universality of Hom Complexes}, author={Anton Dochtermann}, year={2007} }

- Published 2007

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.