Homology, Homotopy and Applications
Volume 24 (2022)
Cellular sheaves of lattices and the Tarski Laplacian
Pages: 325 – 345
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.
cellular sheaves, lattice theory, non-abelian homological algebra
2010 Mathematics Subject Classification
05C50, 18B35, 18F20, 55N30
Copyright © 2022, Robert Ghrist and Hans Riess. Permission to copy for private use granted.
Received 13 July 2020
Received revised 21 April 2021
Accepted 26 April 2021
Published 13 April 2022