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Toric Orbit Spaces Which are Manifolds
Arnold Mathematical Journal. 2024. P. 0.
Ayzenberg A., Gorchakov V.
Ероховец Н. Ю., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 326 С. 193–239
We consider (not necessarily free) actions of subgroups H⊂Z_2^m on the real moment–angle manifold RZ_P corresponding to a simple convex n-polytope P with m facets. A criterion for the orbit space RZ_P/H to be a topological manifold (perhaps with boundary) can be extracted from results by M. A. Mikhailova and C. Lange. For any dimension n we construct a series of manifolds RZ_P/H homeomorphic to S^n and a series of manifolds M^n=RZ_P/H admitting a hyperelliptic involution τ∈Z_2^m/H, that is, an ...
Added: November 26, 2025
Gorchakov V., Journal of the Mathematical Society of Japan 2025
Added: May 22, 2025
Barinova M., Osenkov E., Pochinka O., Regular and Chaotic Dynamics 2025 Vol. 30 No. 2 P. 226–253
In investigating dynamical systems with chaotic attractors, many aspects of global behavior of a flow or a diffeomorphism with such an attractor are studied by replacing a nontrivial attractor by a trivial one [1, 2, 11, 14]. Such a method allows one to reduce the original system to a regular system, for instance, of a Morse – Smale ...
Added: April 8, 2025
Ayzenberg A., Труды Математического института им. В.А. Стеклова РАН 2018 Т. 302 С. 23–40
We consider an effective action of a compact (n-1)-torus on a smooth 2n-manifold with isolated xed points. We prove that under certain conditions the orbit space is a closed topological manifold. In particular, this holds for certain torus actions with disconnected stabilizers. There is a ltration of the orbit manifold by orbit dimensions. The subset ...
Added: October 15, 2018