Finite quotients of Bruhat-Tits buildings as geometric expanders

Shai Evra*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In [5], Fox, Gromov, Lafforgue, Naor and Pach, in a response to a question of Gromov [7], constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit constructions are finite quotients of A d-buildings, for d ≥ 2, over local fields. In this paper, this result is extended to general high rank Bruhat-Tits buildings.

Original languageAmerican English
Pages (from-to)51-66
Number of pages16
JournalJournal of Topology and Analysis
Volume9
Issue number1
DOIs
StatePublished - 1 Mar 2017

Bibliographical note

Publisher Copyright:
© 2017 World Scientific Publishing Company.

Keywords

  • Bruhat-Tits buildings
  • Hecke operators
  • High-dimensional expanders
  • geometric expanders
  • overlapping property
  • property (T)

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