Local spectral expansion approach to high dimensional expanders
Combinatorics
2015-03-26 v4
Abstract
This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We show the condition of local spectral expansion has several nice implications. For example, for a simplicial complex with local spectral expansion we show vanishing of cohomology with real coefficients, Cheeger type inequalities and mixing type results and geometric overlap results.
Cite
@article{arxiv.1407.8517,
title = {Local spectral expansion approach to high dimensional expanders},
author = {Izhar Oppenheim},
journal= {arXiv preprint arXiv:1407.8517},
year = {2015}
}
Comments
96 pages. This version has minor corrections regarding the result of mixing for partite complexes