A Model for Random Chain Complexes

Abstract

We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over ${\mathbb{F}}_q$, conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.

arXiv comment9 pages, comments welcome