TY - GEN

T1 - Swap Cosystolic Expansion

AU - Dikstein, Yotam

AU - Dinur, Irit

N1 - Publisher Copyright:
© 2024 Copyright is held by the owner/author(s). Publication rights licensed to ACM.

PY - 2024/6/10

Y1 - 2024/6/10

N2 - We introduce and study swap cosystolic expansion, a new expansion property of simplicial complexes. We prove lower bounds for swap coboundary expansion of spherical buildings and use them to lower bound swap cosystolic expansion of the LSV Ramanujan complexes. Our motivation is the recent work (in a companion paper) showing that swap cosystolic expansion implies agreement theorems. Together the two works show that these complexes support agreement tests in the low acceptance regime. We also study the closely related swap coboundary expansion. Swap cosystolic expansion is defined by considering, for a given complex X, its faces complex , whose vertices are r-faces of X and where two vertices are connected if their disjoint union is also a face in X. The faces complex is a derandomization of the product of X with itself r times. The graph underlying is the swap walk of X, known to have excellent spectral expansion. The swap cosystolic expansion of X is defined to be the cosystolic expansion of . Our main result is a exp(-O(√r)) lower bound on the swap coboundary expansion of the spherical building and the swap cosystolic expansion of the LSV complexes. For more general coboundary expanders we show a weaker lower bound of exp(-O(r)).

AB - We introduce and study swap cosystolic expansion, a new expansion property of simplicial complexes. We prove lower bounds for swap coboundary expansion of spherical buildings and use them to lower bound swap cosystolic expansion of the LSV Ramanujan complexes. Our motivation is the recent work (in a companion paper) showing that swap cosystolic expansion implies agreement theorems. Together the two works show that these complexes support agreement tests in the low acceptance regime. We also study the closely related swap coboundary expansion. Swap cosystolic expansion is defined by considering, for a given complex X, its faces complex , whose vertices are r-faces of X and where two vertices are connected if their disjoint union is also a face in X. The faces complex is a derandomization of the product of X with itself r times. The graph underlying is the swap walk of X, known to have excellent spectral expansion. The swap cosystolic expansion of X is defined to be the cosystolic expansion of . Our main result is a exp(-O(√r)) lower bound on the swap coboundary expansion of the spherical building and the swap cosystolic expansion of the LSV complexes. For more general coboundary expanders we show a weaker lower bound of exp(-O(r)).

KW - Coboundary Expansion

KW - Cocycle Expanders

KW - Cosystolic Expanders

KW - Covers

KW - HDX

KW - High Dimensional Expanders

UR - http://www.scopus.com/inward/record.url?scp=85196636367&partnerID=8YFLogxK

U2 - 10.1145/3618260.3649780

DO - 10.1145/3618260.3649780

M3 - Conference contribution

AN - SCOPUS:85196636367

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1956

EP - 1966

BT - STOC 2024 - Proceedings of the 56th Annual ACM Symposium on Theory of Computing

A2 - Mohar, Bojan

A2 - Shinkar, Igor

A2 - O�Donnell, Ryan

PB - Association for Computing Machinery

T2 - 56th Annual ACM Symposium on Theory of Computing, STOC 2024

Y2 - 24 June 2024 through 28 June 2024

ER -