TL;DR
This paper extends Morse theoretic techniques to all 1-skeleta, demonstrating that previously known conditions for constructing equivariant cohomology bases are universally applicable.
Contribution
It proves that Guillemin and Zara's conditions for Morse theory on 1-skeleta hold universally, regardless of independence or GKM properties.
Findings
Conditions are valid for all 1-skeleta.
Morse theoretic methods apply broadly beyond GKM cases.
Supports universal applicability of Morse techniques in equivariant cohomology.
Abstract
Guillemin and Zara gave necessary and sufficient conditions under which Morse theoretic techniques could be used to construct an additive basis for the equivariant cohomology of a 1-skeleton that is either 3-independent or GKM. We show that their conditions remain valid for all 1-skeleta, 3-independent, GKM, or otherwise.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models