Simplicial Complexes and Laplacians
From CanisiusmathWiki
Abstract: The Laplacian operator on a simplicial complex encodes information about the adjacencies between the simplices of common dimensions. Since the Laplacian is not a topological invariant, we look for relationships between simplicial complexes that might translate to relationships between their Laplacians. We found that one such relationship is that of a covering of a simplicial complex, which is a larger complex that contains the same adjacency relationships between its simplices. We show that the Laplacian spectrum of a complex is contained inside the Laplacian spectrum of any of its covering complexes.
Simplicial Complexes and Bistellar Moves
Laplacians and Covering Complexes
Laplacians of Neighborhood Complexes
The Edgepath Group and Order Complexes
