The reviewed record of science sign in
Pith

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

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel pith:UDT3RPHNrecord.jsonopen to challenge →

classification math.AT math.CTmath.RA
keywords applicationscellularlaplacianlatticessheavestarskiagreesbroader
0
0 comments X
read the original abstract

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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Representing Higher-Order Networks: A Survey of Graph-Based Frameworks

    cs.SI 2026-03 unverdicted novelty 4.0

    A comprehensive survey of graph-based frameworks for higher-order networks, covering foundational concepts, extensions, and newly introduced formalisms with emphasis on structural principles and applications.

  2. Representing Higher-Order Networks: A Survey of Graph-Based Frameworks

    cs.SI 2026-03 unverdicted novelty 2.0

    A comprehensive survey of graph-based formalisms for higher-order networks including multiway, hierarchical, temporal, multilayer, recursive, and tensor-based models.