English

The universality of Hom complexes

Combinatorics 2007-05-23 v1 Algebraic Topology

Abstract

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.

Keywords

Cite

@article{arxiv.math/0702471,
  title  = {The universality of Hom complexes},
  author = {Anton Dochtermann},
  journal= {arXiv preprint arXiv:math/0702471},
  year   = {2007}
}

Comments

14 pages, 12 figures

R2 v1 2026-07-22T17:51:11.082Z