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Abstract

The h The hom complex Hom(G,K) is the order complex of the poset composed of the graph multihomomorphisms from G to K. We use homology to provide conditions under which the hom complex is not contractible and derive a lower bound on the rank of its homology groups.om complex Hom(G,K) is the order complex of the poset composed of the graph multihomomorphisms from G to K. We use homology to provide conditions under which the hom complex is not contractible and derive a lower bound on the rank of its homology groups.

Author Bio

Mychael Sanchez is a PhD student in the mathematics department at the University of Illinois. His undergraduate research was supervised by Dr. Daniel Ramras. He began this research project during the fall of 2009 and worked with Dr. Ramras until his graduation in Spring 2011. His mathematical interests are in algebraic topology; specifically, he is interested in homotopy theory and applications to algebraic geometry. He is an avid basketball player in his spare time.

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