2020/03/21 by Iván Contreras, Contreras, Ivan, Andrew Rosevear +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2003.09704
openalex publication_date 2020/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a graph-theoretical interpretation of an induced action of Aut(Γ) in the discrete de Rham cohomology of a finite graph Γ. This action produces a splitting of Aut(Γ) that depends on the cycles of Γ. We also prove some graph-theoretical analogues of standard results in differential geometry, in particular, a graph version of Stokes' Theorem and the Mayer-Vietoris sequence in cohomology.