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Local spectral expansion approach to high dimensional expanders (1407.8517v4)
Published 31 Jul 2014 in math.CO
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.
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