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arxiv: 2007.04099 · v2 · pith:UDT3RPHN · submitted 2020-07-08 · math.AT · math.CT· math.RA

Cellular Sheaves of Lattices and the Tarski Laplacian

Robert Ghrist , Hans Riess This is my paper

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classification math.AT math.CTmath.RA
keywords applicationscellularlaplacianlatticessheavestarskiagreesbroader
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This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a cohomology that agrees with the global section functor in degree zero. This has immediate applications in consensus and distributed optimization problems over networks and broader potential applications.

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