Bounded Degree Cosystolic Expanders of Every Dimension

TL;DR

This paper introduces a new criterion for high-dimensional cosystolic expansion and applies it to Ramanujan complexes, producing infinite families of bounded degree complexes with topological overlapping, answering an open question by Gromov.

Contribution

It presents a novel local-to-global criterion for cosystolic expansion and constructs infinite bounded degree complexes with topological overlap in all dimensions.

Findings

Established a new criterion for high-dimensional cosystolic expansion.

Constructed infinite families of bounded degree complexes with topological overlap.

Answered Gromov's open question affirmatively.

Abstract

In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan complexes, yields for every dimension, an infinite family of bounded degree complexes with the topological overlapping property. This answer affirmatively an open question raised by Gromov.