On isomorphisms between fibrations over associated with a action
Michał Sadowski (1991)
Annales Polonici Mathematici
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Michał Sadowski (1991)
Annales Polonici Mathematici
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Pedro L. Q. Pergher, Rogério de Oliveira (2008)
Fundamenta Mathematicae
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Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property when it has the following property: if is any smooth closed m-dimensional manifold with m > n and is a smooth involution whose fixed point set is Fⁿ, then m = 2n. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces , and , and the connected sum of and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere...
Pedro L. Q. Pergher, Rogério de Oliveira (2005)
Fundamenta Mathematicae
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Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if is any smooth and closed m-dimensional manifold with m > n and is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions of the group on closed smooth m-dimensional manifolds for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....
John Kalliongis, Ryo Ohashi (2017)
Commentationes Mathematicae Universitatis Carolinae
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We describe the finite group actions, up to equivalence, which can act on the orbifold , and their quotient types. This is then used to consider actions on prism manifolds which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If is such an action, we show that and fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by . For the standard actions, we compute the fundamental group of and...
Taher Bichr (2021)
Czechoslovak Mathematical Journal
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Let be the space of linear differential operators on weighted densities from to as module over the orthosymplectic Lie superalgebra , where , is the space of tensor densities of degree on the supercircle . We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.
T. E. Barros, C. Biasi (2008)
Colloquium Mathematicae
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Let p be a prime number and X a simply connected Hausdorff space equipped with a free -action generated by . Let be a homeomorphism generating a free -action on the (2n-1)-sphere, whose orbit space is some lens space. We prove that, under some homotopy conditions on X, there exists an equivariant map . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.
Sergei Yu. Pilyugin, Sergei B. Tikhomirov (2003)
Fundamenta Mathematicae
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We study shadowing properties of continuous actions of the groups and . Necessary and sufficient conditions are given under which a linear action of on has a Lipschitz shadowing property.
Adrian Ioana (2009)
Annales scientifiques de l'École Normale Supérieure
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For any , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group . These actions arise as diagonal products between a generalized Bernoulli action and the action , where is seen as a subgroup of .
Michael G. Megrelishvili, Tzvi Scarr (2001)
Fundamenta Mathematicae
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Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding ; (2) there exists an embedding , equivariant with respect to φ, such that ψ(X) is an equivariant retract of with respect...
Dave Anderson, Stephen Griffeth, Ezra Miller (2011)
Journal of the European Mathematical Society
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We prove the conjectures of Graham–Kumar [GrKu08] and Griffeth–Ram [GrRa04] concerning the alternation of signs in the structure constants for torus-equivariant -theory of generalized flag varieties . These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a natural group action with finitely many orbits. The computation of the coefficients in the expansion...
Stefaan Vaes (2008)
Annales scientifiques de l'École Normale Supérieure
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We study II factors and associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index --bimodule (in particular, every isomorphism between and ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index --bimodules is identified with an extended Hecke fusion algebra,...
Bruno P. Zimmermann (2014)
Fundamenta Mathematicae
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Let denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on which is quadratic in g. For the proofs we develop a calculus...
Philippe Bonnet (2003)
Bulletin de la Société Mathématique de France
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Let be a polynomial dominating map from to . We study the quotient of polynomial 1-forms that are exact along the generic fibres of , by 1-forms of type , where are polynomials. We prove that is always a torsion -module. Then we determine under which conditions on we have . As an application, we study the behaviour of a class of algebraic -actions on , and determine in particular when these actions are trivial.
Witold Kondracki, Jan Rogulski
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CONTENTSIntroduction..................................................................................................................................................5§1. Basic notions and notation.....................................................................................................................7 1.1. Automorphisms of principal bundles....................................................................................................7 1.2. Connections and parallel...
(2025)
Archivum Mathematicum
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Ted Chinburg, Robert Guralnick, David Harbater (2011)
Annales scientifiques de l'École Normale Supérieure
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Let be an algebraically closed field of characteristic . We study obstructions to lifting to characteristic the faithful continuous action of a finite group on . To each such a theorem of Katz and Gabber associates an action of on a smooth projective curve over . We say that the KGB obstruction of vanishes if acts on a smooth projective curve in characteristic in such a way that and have the same genus for all subgroups . We determine for which the KGB...
Daniel Skodlerack (2013)
Annales de l’institut Fourier
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Let be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let be the centralizer of a semisimple rational Lie algebra element of We prove that the Bruhat-Tits building of can be affinely and -equivariantly embedded in the Bruhat-Tits building of so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let and be maps from to which preserve the Moy–Prasad filtrations....
Zhiqi Chen, Jifu Li, Ming Ding (2022)
Czechoslovak Mathematical Journal
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-manifold algebras are focused on the algebraic properties of the tangent sheaf of -manifolds. The local classification of 3-dimensional -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional -manifold algebras over the complex field .
Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)
Annales scientifiques de l'École Normale Supérieure
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Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
T. E. Barros (2001)
Bulletin de la Société Mathématique de France
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In [R] explicit representatives for -principal bundles over are constructed, based on these constructions explicit free -actions on the total spaces are described, with quotients exotic -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic -spheres that occur as quotients of the free -actions described...