The Laplace operator on a simplicial complex encodes information about the adjacencies between simplices. A relationship between simplicial complexes does not always translate to a relationship between their Laplacians. In this paper we look at the case of covering complexes. A covering of a simplicial complex is built from many copies of simplices of the original complex, maintaining the adjacency relationships between simplices. We show that for dimension at least one, the Laplacian spectrum of a simplicial complex is contained inside the Laplacian spectrum of any of its covering complexes.

Author Bio

I am currently a first year graduate student at the City University of NewYork Graduate Center, studying combinatorics. I graduated from CornellUniversity in May 2011 with a Bachelor of Arts in Mathematics. I performed this research as part of an REU program held at Canisius College inthe summer of 2010, where I worked with Dr. Terrence Bisson. I plan onreceiving a Ph.D. in Mathematics and teaching at the university level.