Computing Betti Numbers via Combinatorial Laplacians

We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a number of advantages over other methods, both in theory and in practice. It requires small storage space in many cases. It seems to run quickly in practice, but its running time depends on a ratio, , of eigenvalues which we have yet to fully understand. We numerically verify a conjecture of Bj

• Type: Conference
• Year: 1996
• Where: STOC
• Authors: Joel Friedman
• Keywords: Algorithms, Betti Numbers, Simplicial Complexes, Small Storage Space, STOC 1996