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Abstract
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We provide an interpretation of the discrete version of Morse inequalities, following
Witten’s approach via supersymmetric quantum mechanics (J. Differential Geom.
17:4 (1982), 661-692), adapted by Forman to finite graphs, as a particular
instance of Morse–Witten theory for cell complexes (Topology 37:5 (1998), 945–979).
We describe the general framework of graph quantum mechanics and we produce
discrete versions of the Hodge theorems and energy cut-offs within this
formulation.
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Keywords
graph Laplacian, Morse–Witten complex, graph Hodge theory,
discrete Morse functions
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Mathematical Subject Classification 2010
Primary: 05C10, 81Q35
Secondary: 94C15
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Milestones
Received: 15 May 2018
Revised: 16 October 2018
Accepted: 18 October 2018
Published: 30 July 2019
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