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Spectra of combinatorial Laplace operators on simplicial complexes
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Horak, Danijela and Jost, Jürgen (2013) Spectra of combinatorial Laplace operators on simplicial complexes. Advances in Mathematics, Volume 244 . pp. 303-336. doi:10.1016/j.aim.2013.05.007 ISSN 0001-8708.
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Official URL: http://dx.doi.org/10.1016/j.aim.2013.05.007
Abstract
We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the weighted Laplacian, and the normalized graph Laplacian. This framework then allows us to define the normalized Laplace operator Delta(up)(i) on simplicial complexes which we then systematically investigate. We study the effects of a wedge sum, a join and a duplication of a motif on the spectrum of the normalized Laplace operator and identify some of the combinatorial features of a simplicial complex that are encoded in its spectrum.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Journal or Publication Title: | Advances in Mathematics | ||||||||||
Publisher: | Academic Press | ||||||||||
ISSN: | 0001-8708 | ||||||||||
Official Date: | 10 September 2013 | ||||||||||
Dates: |
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Volume: | Volume 244 | ||||||||||
Page Range: | pp. 303-336 | ||||||||||
DOI: | 10.1016/j.aim.2013.05.007 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access |
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