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Индекс 1-формы на вещественной фактор-особенности
Функциональный анализ и его приложения. 2018. Т. 52. № 2. С. 78-81.
Let G be a finite Abelian group acting (linearly) on space ℝn and, therefore, on its complexification ℂn, and let W be the real part of the quotient ℂn/G (in the general case, W ≠ ℝn/G). The index of an analytic 1-form on the space W is expressed in terms of the signature of the residue bilinear form on the G-invariant part of the quotient of the space of germs of n-forms on (ℝn, 0) by the subspace of forms divisible by the 1-form under consideration.
Gusein-Zade S., Mathematische Nachrichten 2018 Vol. 291 No. 17-18 P. 2543-2556
Let a finite abelian group G act (linearly) on the space R^n and thus on its complexification C^n. Let W be the real part of the quotient C^n/G (in general W \neq R^n/G). We give an algebraic formula for the radial index of a 1-form \omega on the real quotient W. It is shown that ...
Added: October 27, 2020
Gusein-Zade S., Алгебра и анализ 2021 Т. 33 № 3 С. 73-84
Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological invariants of spaces with some additional structures) are sometimes related with corresponding analogues of indices of singular points. Earlier, there was defined ...
Added: May 2, 2021
Gusein-Zade S., Раух А. Я., Функциональный анализ и его приложения 2021 Т. 55 № 1 С. 56-64
V.I.Arnold classified simple (i.e. having no moduli for the classification) singularities (function germs) and also simple boundary singularities: function germs invariant with respect to the action
σ(x1;y1,…,yn)=(−x1;y1,…,yn) of the group Z2. In particular, it was shown that a function germ (a germ of a boundary singularity) is simple if and only if the intersection form (respectively, ...
Added: February 3, 2021
Kleptsyn V., Alvarez S., Malicet D. et al., / Cornell University. Series math "arxiv.org". 2015.
Added: June 22, 2016
Gusein-Zade S., Journal of Algebra and its Applications 2018 Vol. 17 No. 10 P. 1-13
In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here, a so-called enhanced Burnside ring Bˆ(G) of a finite group G is defined. An ...
Added: October 27, 2020
Gusein-Zade S., Математические заметки 2020 Т. 107 № 6 С. 855-864
V.I.Arnold has classified simple (i.e., having no moduli for the classification) singularities (function germs), and also simple boundary singularities: function germs invariant with respect to the action σ (x1; y1, …, yn) = (−x1; y1, …, yn) of the group ℤ2. In particular, it was shown that a function germ (a boundary singularity germ) is ...
Added: October 27, 2020
Babenko A., IEEE Transactions on Pattern Analysis and Machine Intelligence 2014 Vol. PP No. 99 P. 1
A new data structure for efficient similarity search in very large datasets of high-dimensional vectors is introduced. This structure called the inverted multi-index generalizes the inverted index idea by replacing the standard quantization within inverted indices with product quantization. For very similar retrieval complexity and pre-processing time, inverted multi-indices achieve a much denser subdivision of ...
Added: December 19, 2014
Filimonov D., Клепцын В. А., Nonlinearity 2014 Vol. 27 No. 6 P. 1205-1223
We study possible one-end finitely presented subgroups of <img />, acting without finite orbits. Our main result, theorem 1, establishes that any such action possesses the so-called property (<img />), that allows one to make distortion-controlled expansion and is thus sufficient to conclude that the action is Lebesgue-ergodic. We also propose a path towards full ...
Added: October 23, 2014
Khristoforov M., Klimenko A. V., Bufetov A. I., International Mathematics Research Notices 2012 No. 21 P. 4797-4829
Cesaro convergence of spherical averages is proven for measurepreserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in Lp, 1 p < 1, and pointwise convergence for functions in L1. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence ...
Added: November 16, 2012
Gusein-Zade S., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2020 Vol. 16 No. 051 P. 1-15
P. Berglund, T. Hübsch, and M. Henningson proposed a method to construct mirror symmetric Calabi–Yau manifolds. They considered a pair consisting of an invertible polynomial and of a finite (abelian) group
of its diagonal symmetries together with a dual pair. A. Takahashi suggested a method to generalize this construction to symmetry groups generated by some diagonal ...
Added: October 27, 2020
Alvarez S., Filimonov D., Kleptsyn V. et al., Journal of Topology 2019 Vol. 12 No. 4 P. 1315-1367
This article is inspired by two milestones in the study of non-minimal group actions on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves, and Ghys' freeness result in real-analytic regularity. Our first result concerns groups of real-analytic diffeomorphisms with infinitely many ends: if the action is non expanding, then the group ...
Added: July 13, 2019
Klimenko A. V., Bufetov A. I., Труды Математического института им. В.А. Стеклова РАН 2012 Т. 277 С. 33-48
Устанавливается сходимость почти всюду средних по Чезаро сферических средних произвольной функции из класса L^p, p>1, для действий марковских полугрупп, и в частности конечно порожденных гиперболических групп. ...
Added: February 13, 2013
Gusein-Zade S., Manuscripta Mathematica 2018 Vol. 155 No. 3-4 P. 335-353
For a germ of a quasihomogeneous function with an isolated critical point at the origin invariant with respect to an appropriate action of a finite abelian group, H. Fan, T. Jarvis, and Y. Ruan defined the so-called quantum cohomology group. It is considered as the main object of the quantum singularity theory (FJRW-theory). We define ...
Added: October 27, 2020
Ebeling W., Gusein-Zade S., Pure and Applied Mathematics Quarterly 2020 Vol. 16 No. 4 P. 1099-1113
In the framework of constructing mirror symmetric pairs of Calabi-Yau manifolds, P.Berglund, T.Hubsch and M.Henningson considered a pair (f,G) consisting of an invertible polynomial f and a finite abelian group G of its diagonal symmetries and associated to this pair a dual pair (f~, G~). A.Takahashi suggested a generalization of this construction to pairs (f, ...
Added: February 3, 2021
Ebeling W., Gusein-Zade S., International Mathematics Research Notices 2021 Vol. 2021 No. 16 P. 12305-12329
A.Takahashi suggested a conjectural method to find mirror symmetric pairs consisting of invertible polynomials and symmetry groups generated by some diagonal symmetries and some permutations of variables. Here we generalize the Saito duality between Burnside rings to a case of non-abelian groups and prove a "non-abelian" generalization of the statement about the equivariant Saito duality ...
Added: August 26, 2021
Bufetov A. I., Klimenko A. V., Христофоров М. И., Успехи математических наук 2011 Т. 66 № 3 С. 203-204
В данной статье нами формулируется теорема о сходимости по Чезаро (в смысле L^p и почти всюду) сферических средних для сохраняющих меру действий марковских групп. ...
Added: February 13, 2013
Arzhantsev I., Romaskevich E., Proceedings of the American Mathematical Society 2017 Vol. 145 No. 5 P. 1865-1879
By an additive action on an algebraic variety of dimension we mean a regular action with an open orbit of the commutative unipotent group . We prove that if a complete toric variety admits an additive action, then it admits an additive action normalized by the acting torus. Normalized additive actions on a toric variety ...
Added: February 22, 2017
Filimonov D., Клепцын В. А., Труды Московского математического общества 2012 Т. 73 № 1 С. 37-46
Мы исследуем класс минимально действующих конечно порождённых групп C2-диффеоморфизмов окружности, для которых имеет место свойство неподвижности нерастяжимых точек, причём множество нерастяжимых точек непусто. Оказывается, показатель Ляпунова растяжения любого такого действия равен нулю. Следствием этого оказывается сингулярность стационарной меры для случайной динамики, заданной любым вероятностным распределением, носитель которого — конечное множество порождающих группу элементов. ...
Added: November 14, 2013
Айзенберг А.А., Бухштабер В.М., Математический сборник 2021 Т. 212 № 5 С. 3-36
Матрицей-стрелкой называется матрица с нулями вне главной диагонали, первой строки и первого столбца. В работе исследуется пространство MStn,λ всех эрмитовых матриц-стрелок размера (n+1)×(n+1), имеющих заданный простой спектр λ. Доказано, что это пространство – гладкое 2n-мерное многообразие с локально стандартным действием тора, описана топология и комбинаторика его пространства орбит. При n⩾3 пространство орбит MStn,λ/Tn не является многогранником, а значит, MStn,λ не является квазиторическим многообразием. Тем не менее на MStn,λ имеется действие полупрямого ...
Added: June 18, 2021
Volk D., Kleptsyn V., Gorodetski A. et al., Moscow Mathematical Journal 2014 Vol. 14 No. 2 P. 291-308
We consider a minimal action of a finitely generated semigroup by homeomorphisms of the circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random ...
Added: December 30, 2015
Попов В. Л., Известия РАН. Серия математическая 2019 Т. 84 № 4 С. 194-225
The rst group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in
other groups. The third concerns the connectedness of the Cremona groups. ...
Added: July 31, 2019
Kazaryan M., Uribe-Vargas R., Moscow Mathematical Journal 2020 Vol. 20 No. 3 P. 511-530
We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. ...
Added: August 24, 2020
Filimonov D., Клепцын В. А., Функциональный анализ и его приложения 2012 Т. 46 № 3 С. 38-61
Работа посвящена исследованию групп диффеоморфизмов окружности со свойством неподвижности нерастяжимых точек. Это свойство обобщает свойство локальной растяжимости, и на текущий момент не известно примеров минимальных действий конечно порожденных групп C2-диффеоморфизмами окружности, которые бы этим свойством не обладали.
Оказывается, что в предположении, что диффеоморфизмы обладают указанным свойством, и при наличии хотя бы одной нерастяжимой точки, действие допускает достаточно ...
Added: November 14, 2013
Agranovich M. S., Айзенберг Л. А., Алфимов Г. Л. et al., Успехи математических наук 2012 Т. 67 № 1 С. 169-177
математический некролог ...
Added: February 22, 2013