-categoricity of generalized products
Jan Waszkiewicz (1973)
Colloquium Mathematicae
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Jan Waszkiewicz (1973)
Colloquium Mathematicae
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Nicolas Monod, Henrik Densing Petersen (2014)
Annales de l’institut Fourier
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Let be any group containing an infinite elementary amenable subgroup and let . We construct an exhaustion of by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to -dimension and gives an answer to a question of Gaboriau.
Mikhail Skopenkov (2003)
Fundamenta Mathematicae
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For any collection of graphs we find the minimal dimension d such that the product is embeddable into (see Theorem 1 below). In particular, we prove that (K₅)ⁿ and are not embeddable into , where K₅ and are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is a reduction to a problem from so-called Ramsey link theory: we show that any embedding , where O is a vertex of (K₅)ⁿ, has a pair of linked (n-1)-spheres.
Fabiano G. B. Brito, Pablo M. Chacón, David L. Johnson (2008)
Bulletin de la Société Mathématique de France
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We establish in this paper a lower bound for the volume of a unit vector field defined on , . This lower bound is related to the sum of the absolute values of the indices of at and .
F. Dai, Z. Ditzian, Hongwei Huang (2010)
Studia Mathematica
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Suppose Δ̃ is the Laplace-Beltrami operator on the sphere and where ρ ∈ SO(d). Then and are equivalent for 1 < p < ∞. We note that for even m the relation was recently investigated by the second author. The equivalence yields an extension of the results on sharp Jackson inequalities on the sphere. A new strong converse inequality for given in this paper plays a significant role in the proof.
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...
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....
Valentina Casarino, Paolo Ciatti (2009)
Studia Mathematica
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By using the notion of contraction of Lie groups, we transfer estimates for joint spectral projectors from the unit complex sphere in to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.
Naotsugu Chinen (2015)
Commentationes Mathematicae Universitatis Carolinae
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By , , we denote the -th symmetric product of a metric space as the space of the non-empty finite subsets of with at most elements endowed with the Hausdorff metric . In this paper we shall describe that every isometry from the -th symmetric product into itself is induced by some isometry from into itself, where is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence...
Francisco Javier González Vieli (2017)
Czechoslovak Mathematical Journal
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Given a distribution on the sphere we define, in analogy to the work of Łojasiewicz, the value of at a point of the sphere and we show that if has the value at , then the Fourier-Laplace series of at is Abel-summable to .
E. Karapınar, M. Yurdakul, V. Zahariuta (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let ℓ be a Banach sequence space with a monotone norm , in which the canonical system is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products where and are finite and infinite ℓ-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by...
Krzysztof Kołodziejczyk (1987)
Colloquium Mathematicae
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Gryzlov, A.
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Th. Friedrich (1974)
Colloquium Mathematicae
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M. Đurić (1973)
Matematički Vesnik
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N. Kalamidas, Th. Zachariades (1989)
Colloquium Mathematicae
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A. Makowski (1964)
Matematički Vesnik
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