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November 2021 On the sign ambiguity in equivariant cohomological rigidity of GKM graphs
Hitoshi Yamanaka
Proc. Japan Acad. Ser. A Math. Sci. 97(9): 76-81 (November 2021). DOI: 10.3792/pjaa.97.015

Abstract

This is the sequel to the author’s previous paper [1] with Matthias Franz. In the present paper, we introduce the notion of equivariant total Chern class of a GKM graph and show that the pair of graph equivariant cohomology and the equivariant total Chern class determines the GKM graph completely. We also show that for a torus graph in the sense of Maeda–Masuda–Panov, the pair of graph equivariant cohomology and the equivariant 1-st Chern class determines the torus graph completely.

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Hitoshi Yamanaka. "On the sign ambiguity in equivariant cohomological rigidity of GKM graphs." Proc. Japan Acad. Ser. A Math. Sci. 97 (9) 76 - 81, November 2021. https://doi.org/10.3792/pjaa.97.015

Information

Published: November 2021
First available in Project Euclid: 4 November 2021

Digital Object Identifier: 10.3792/pjaa.97.015

Subjects:
Primary: 55N91
Secondary: 57S12

Keywords: equivariant cohomological rigidity , equivariant total Chern class , GKM graph , torus graph

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 9 • November 2021
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