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Equivariant cohomology of torus orbifolds

Part of: Special varieties Differential topology Arithmetic rings and other special rings Homology and cohomology theories

Published online by Cambridge University Press:  20 November 2020

Alastair Darby ,
Shintarô Kuroki  and
Jongbaek Song
Alastair Darby
Affiliation:
Department of Pure Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, China e-mail: Alastair.Darby@xjtlu.edu.cn
Shintarô Kuroki
Affiliation:
Department of Applied Mathematics, Okayama University of Science, Okayama, Japan email: kuroki@xmath.ous.ac.jp
Jongbaek Song*
Affiliation:
School of Mathematics, KIAS, Seoul, Republic of Korea
*
e-mail: jongbaek.song@gmail.com
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Abstract

We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin by studying GKM-orbifolds, which are more general, before specializing to half-dimensional torus actions.

Keywords

GKM-orbifoldtorus orbifoldequivariant cohomologyGKM-theoryface ring

MSC classification

Primary: 14M25: Toric varieties, Newton polyhedra
Secondary: 55N91: Equivariant homology and cohomology 57R18: Topology and geometry of orbifolds 13F55: Stanley-Reisner face rings; simplicial complexes
Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 2 , April 2022 , pp. 299 - 328
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

A.D. was supported by XJTLU RDF-17-02-50. S.K. was supported by JSPS KAKENHI Grant Number 17K14196. J.S. has been supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048480) and a KIAS Individual Grant (MG076101) at Korea Institute for Advanced Study.

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