Geodesic
Cellular sheaves of lattices and the Tarski Laplacian
Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 325-345.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2022.v24.n1.a16
Classification : 05C50, 18B35, 18F20, 55N30
Keywords: cellular sheaves, lattice theory, non-abelian homological algebra 
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Robert Ghrist; Hans Riess. Cellular sheaves of lattices and the Tarski Laplacian. Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 325-345. doi : 10.4310/HHA.2022.v24.n1.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a16/

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