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Equivariantly formal 2-torus actions of complexity one
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
Arzhantsev I., Chuvashova O. V., Sbornik Mathematics 2004 Vol. 195 No. 6 P. 765–782
The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. Affine homogeneous spaces G/H of complexity 1 are classified in this paper. These results are the natural continuation of the earlier classification ...
Added: June 13, 2025
Arzhantsev I., Izvestiya. Mathematics 1997 Vol. 61 No. 4 P. 685–698
This paper is devoted to the actions of the group SL(2) with two-dimensional generic orbit on normal three-dimensional affine algebraic varieties. We obtain a complete classi cation of such actions whenever the stabilizer of general position
is the subgroup of monomial matrices. We also prove some results for arbitrary actions of complexity one of reductive groups. ...
Added: June 13, 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., Gorchakov V., Arnold Mathematical Journal 2024 P. 0
Added: May 30, 2024
Panov T., Зейникешева И. К., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 317 С. 157–167
We compute the equivariant cohomology $H^*_{T_I}(Z_K)$ of moment-angle complexes $Z_K$ with respect to the action of coordinate subtori $T_I \subset T^m$. We give a criterion for the equivariant formality of $Z_K$ and obtain specifications for the cases of flag complexes and graphs. ...
Added: November 11, 2022