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 (2002)
Fundamenta Mathematicae
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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 the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally,...
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....
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...
William A. Webb (1990)
Colloquium Mathematicae
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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.
Carlos Biasi, Alice K. M. Libardi, Pedro L. Q. Pergher, Stanisław Spież (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let E be an oriented, smooth and closed m-dimensional manifold with m ≥ 2 and V ⊂ E an oriented, connected, smooth and closed (m-2)-dimensional submanifold which is homologous to zero in E. Let be the standard inclusion, where Sⁿ is the n-sphere and n ≥ 3. We prove the following extension result: if is a smooth map, then h extends to a smooth map g: E → Sⁿ transverse to and with . Using this result, we give a new and simpler proof of a theorem of Carlos Biasi related to the ambiental...
D. Kastler (1968)
Recherche Coopérative sur Programme n°25
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Adam Grygiel (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let K be a field and let L = K[ξ] be a finite field extension of K of degree m > 1. If f ∈ L[Z] is a polynomial, then there exist unique polynomials such that . A. Nowicki and S. Spodzieja proved that, if K is a field of characteristic zero and f ≠ 0, then have no common divisor in of positive degree. We extend this result to the case when L is a separable extension of a field K of arbitrary characteristic. We also show that the same is true for a formal power series in several...
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...
Daniel J. Katz, Philippe Langevin (2015)
Acta Arithmetica
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We consider Weil sums of binomials of the form , where F is a finite field, ψ: F → ℂ is the canonical additive character, , and . If we fix F and d, and examine the values of as a runs through , we always obtain at least three distinct values unless d is degenerate (a power of the characteristic of F modulo ). Choices of F and d for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if F is a field of order 3ⁿ with n...
Jian-Ping Fang (2016)
Czechoslovak Mathematical Journal
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We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our results. Using the identities obtained in this paper, we give two interesting identities involving binomial...
Benjamin Dupuy (2007)
Acta Arithmetica
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Laurent Berger (2014)
Journal de l’École polytechnique — Mathématiques
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Let be a finite extension of . The field of norms of a -adic Lie extension is a local field of characteristic which comes equipped with an action of . When can we lift this action to characteristic , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of -modules, and give a condition for the existence of certain types of lifts.
Shyamal Kumar Hui, Debabrata Chakraborty (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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The object of the present paper is to study -Ricci solitons on -Einstein -manifolds. It is shown that if is a recurrent torse forming -Ricci soliton on an -Einstein -manifold then is (i) concurrent and (ii) Killing vector field.
Krzysztof Drachal (2015)
Czechoslovak Mathematical Journal
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This paper is about some geometric properties of the gluing of order in the category of Sikorski differential spaces, where is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour...
D. Przeworska-Rolewicz, S. Rolewicz (1967)
Annales Polonici Mathematici
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Thomas Ernst (2007)
Rendiconti del Seminario Matematico della Università di Padova
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Jana Maříková (2010)
Fundamenta Mathematicae
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Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V → k. Let be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in and conditions on (R,V) which imply o-minimality of . We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in are exactly the standard parts of the sets definable in (R,V).
Kotaro Mine, Katsuro Sakai, Masato Yaguchi (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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By Fin(X) (resp. ), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes and of weight ≤ τ (α > 0) then Fin(E) and each are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X)...
Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)
Commentationes Mathematicae Universitatis Carolinae
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This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux...
Zhi-Wei Sun, Mao-Hua Le (2001)
Acta Arithmetica
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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...