Abstract:
In this paper we study the actions of tori (standard compact tori, as well as their quaternionic analogues) on products of spheres. It is proved 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 a real torus $\mathbb{Z}_2^n$ was proved by the second author in 2019. We also provide a statement about arbitrary compact topological groups, generalizing all the mentioned results, as well as results of the first author about the actions of a compact torus of complexity one. Sections 1 and 2 are written by D.Gugnin, Section 3 is written by A.Ayzenberg.
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 Steklov Mathematical Institute of Russian Academy of Sciences. The work of A.A.Ayzenberg was prepared within the framework of the project "Mirror Laboratories" HSE University, RF.
Citation:
A. A. Ayzenberg, D. 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
\Bibitem{AyzGug24}
\by A.~A.~Ayzenberg, D.~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}
Citation in format AMSBIB
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