Finite quotients of Bruhat-Tits buildings as geometric expanders

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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 languageEnglish (US)
Pages (from-to)51-66
Number of pages16
JournalJournal of Topology and Analysis
Volume9
Issue number1
DOIs
StatePublished - Mar 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Keywords

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

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