The existence of generating families for the cohomology ring of a graph

DOI10.1016/S0001-8708(02)00057-9zbMath1020.57014MaRDI QIDQ1869024

Victor W. Guillemin, Catalin Zara

Publication date: 9 April 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

equivariant cohomology1-skeletonGKM manifoldtorus action on a graph

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Planar graphs; geometric and topological aspects of graph theory (05C10) Momentum maps; symplectic reduction (53D20)

Related Items

Manifolds associated with (2)n+1$(\mathbb {Z}_2)^{n+1}$-colored regular graphs, Generalized 1-skeleta and a lifting result, Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties, Permutation actions on quiver Grassmannians for the equioriented cycle via GKM-theory, Generalized splines on graphs with two labels and polynomial splines on cycles, Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes, Graphs admitting only constant splines

Cites Work

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• Equivariant cohomology, Koszul duality, and the localization theorem
• Equivariant de Rham theory and graphs
• 1-skeleta, Betti numbers, and equivariant cohomology
• Symplectic cuts
• The cohomology rings of symplectic quotients