Equivariant cohomology of even-dimensional complex quadrics from a combinatorial point of view

The purpose of this paper is to determine the ring structure of the graph equivariant cohomology of the GKM graph induced from the even-dimensional complex quadrics. We show that the graph equivariant cohomology is generated by two types of subgraphs in the GKM graph, which are subject to four diffe...

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Bibliographic Details
Published inarXiv.org
Main Author Kuroki, Shintaro
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.07.2024
Subjects
Combinatorial analysis
Graph theory
Homology
Ring structures
Toruses
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Summary:The purpose of this paper is to determine the ring structure of the graph equivariant cohomology of the GKM graph induced from the even-dimensional complex quadrics. We show that the graph equivariant cohomology is generated by two types of subgraphs in the GKM graph, which are subject to four different types of relations. By utilizing this ring structure, we establish the multiplicative relation for the generators of degree 2n and provide an alternative computation of the ordinary cohomology ring of 4n-dimensional complex quadrics, as previously computed by H. Lai. Additionally, we provide a combinatorial explanation for why the square of the 2n degree generator x vanishes when n is odd and is non-vanishing when n is even.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422