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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 326, Pages 5–14
DOI: https://doi.org/10.4213/tm4412 (Mi tm4412) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Actions of Tori and Quaternionic Tori on Products of Spheres

Anton A. Ayzenberga, Dmitry V. Gugninbc

a International Laboratory of Algebraic Topology and Its Applications, Faculty of Computer Science, HSE University, Moscow, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
c Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/tm4412
Abstract: We study the actions of tori (standard compact tori as well as their quaternionic analogs) on products of spheres. We prove that the orbit space of a specific action of a torus on a product of spheres is homeomorphic to a sphere. A similar statement for the real torus Zn2 was proved by the second author in 2019. We also extend this result to arbitrary compact topological groups, thus generalizing the results mentioned above as well as the results of the first author on the actions of a compact torus of complexity 1.
Keywords: torus action, quaternions, orbit space.
Funding agency Grant number
Russian Science Foundation 23-11-00143
HSE Basic Research Program
The work of A. A. Ayzenberg was supported by the project “Mirror Laboratories” at HSE University. The work of D. V. Gugnin was supported by the Russian Science Foundation under grant no. 23-11-00143, https://rscf.ru/en/project/23-11-00143/, and performed at the Steklov Mathematical Institute of Russian Academy of Sciences. Sections 1 and 2 of the paper were written by D. V. Gugnin, and Section 3 was written by A. A. Ayzenberg.
Received: September 29, 2023
Revised: April 30, 2024
Accepted: May 23, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 326, Pages 1–10
DOI: https://doi.org/10.1134/S0081543824040011
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Anton A. Ayzenberg, Dmitry V. Gugnin, “On Actions of Tori and Quaternionic Tori on Products of Spheres”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 5–14; Proc. Steklov Inst. Math., 326 (2024), 1–10
Citation in format AMSBIB
\Bibitem{AyzGug24}
\by Anton~A.~Ayzenberg, Dmitry~V.~Gugnin
\paper On Actions of Tori and Quaternionic Tori on Products of Spheres
\inbook Topology, Geometry, Combinatorics, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 326
\pages 5--14
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4412}
\crossref{https://doi.org/10.4213/tm4412}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 326
\pages 1--10
\crossref{https://doi.org/10.1134/S0081543824040011}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-86000215991}
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  • https://doi.org/10.4213/tm4412
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    • This publication is cited in the following 1 articles:
    1. Nikolai Yu. Erokhovets, “Manifolds Realized as Orbit Spaces of Non-free Zk2-Actions on Real Moment–Angle Manifolds”, Proc. Steklov Inst. Math., 326 (2024), 177–218  mathnet  crossref  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    Abstract page:289
    References:14
    First page:10
     
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