The Universality of Hom Complexes
نویسنده
چکیده
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.
منابع مشابه
The universality of Hom complexes of graphs
It is shown that given a connected graph T with at least one edge and an arbitrary finite simplicial complex X, 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 of graphs, and subdivisions are established that may be of independent interest.
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تاریخ انتشار 2007