Bounded Degree Cosystolic Expanders of Every Dimension

2015/10/03 by Shai Evra, Evra, Shai, Tali Kaufman +1 · 6 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #Computational Complexity (cs.CC) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1510.00839

openalex publication_date 2015/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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