Local Spectral Expansion Approach to High Dimensional Expanders Part I: Descent of Spectral Gaps

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Abstract

We introduce the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various spectral gaps in both the links of the complex and the global Laplacians of the complex.

Original languageEnglish
Pages (from-to)293-330
Number of pages38
JournalDiscrete and Computational Geometry
Volume59
Issue number2
DOIs
StatePublished - 1 Mar 2018

Keywords

  • Graph Laplacian
  • High dimensional expanders
  • Simplicial complexes
  • Spectral gap

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