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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 317, Pages 157–167
DOI: https://doi.org/10.4213/tm4282 (Mi tm4282) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Equivariant Cohomology of Moment–Angle Complexes with Respect to Coordinate Subtori

Taras E. Panovabcd, Indira K. Zeinikeshevaba

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
c Faculty of Computer Science, HSE University, Pokrovskii bul. 11, Moscow, 109028 Russia
d Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
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DOI: https://doi.org/10.4213/tm4282
Abstract: We compute the equivariant cohomology $H^*_{T_I}(\mathcal Z_{\mathcal K})$ of moment–angle complexes $\mathcal Z_{\mathcal K}$ with respect to the action of coordinate subtori $T_I \subset T^m$. We give a criterion for $\mathcal Z_{\mathcal K}$ to be equivariantly formal, and obtain specifications for the cases of flag complexes and graphs.
Keywords: moment–angle complex, equivariant cohomology, equivariant formality, graded modules over polynomial rings.
Funding agency Grant number
Russian Science Foundation 20-11-19998
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-265
The work of the first author (Sections 1–3) was supported by the Russian Science Foundation under grant no. 20-11-19998, https://rscf.ru/project/20-11-19998/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences. The work of the second author (Section 4) was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-265).
Received: April 6, 2022
Revised: May 29, 2022
Accepted: May 30, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 317, Pages 141–150
DOI: https://doi.org/10.1134/S0081543822020079
Bibliographic databases:
Document Type: Article
UDC: 515.14+515.16
MSC: Primary 57S12; Secondary 13F55, 16E45, 55N91, 55R91
Language: Russian
Citation: Taras E. Panov, Indira K. Zeinikesheva, “Equivariant Cohomology of Moment–Angle Complexes with Respect to Coordinate Subtori”, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Collected papers, Trudy Mat. Inst. Steklova, 317, Steklov Math. Inst., М., 2022, 157–167; Proc. Steklov Inst. Math., 317 (2022), 141–150
Citation in format AMSBIB
\Bibitem{PanZei22}
\by Taras~E.~Panov, Indira~K.~Zeinikesheva
\paper Equivariant Cohomology of Moment--Angle Complexes with Respect to Coordinate Subtori
\inbook Toric Topology, Group Actions, Geometry, and Combinatorics. Part~1
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 317
\pages 157--167
\publ Steklov Math. Inst.
\publaddr М.
\mathnet{http://mi.mathnet.ru/tm4282}
\crossref{https://doi.org/10.4213/tm4282}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 317
\pages 141--150
\crossref{https://doi.org/10.1134/S0081543822020079}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85141955288}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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