On isomorphisms between fibrations over $T^k$ associated with a $T^k$ action

Michał Sadowski

Displaying similar documents to “On isomorphisms between fibrations over $T^{k}$ associated with a $T^{k}$ action”

Commuting involutions whose fixed point set consists of two special components

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 $N^{m}$ is any smooth closed m-dimensional manifold with m > n and $T : N^{m} \to N^{m}$ 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 $R P^{2 n}$ , $C P^{2 n}$ and $H P^{2 n}$ , and the connected sum of $R P^{2 n}$ and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere...

$Z ₂^{k}$ -actions fixing point ∪ Vⁿ

Pedro L. Q. Pergher (2002)

Fundamenta Mathematicae

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We describe the equivariant cobordism classification of smooth actions $(M^{m}, Φ)$ of the group $G = Z ₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ 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,...

$Z ₂^{k}$ -actions with a special fixed point set

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 $N^{m}$ is any smooth and closed m-dimensional manifold with m > n and $T : N^{m} \to N^{m}$ is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions $(M^{m}; Φ)$ of the group $G = Z ₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam

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 $ℤ_{p}$ -action generated by $f_{p} : X \to X$ . Let $α : S^{2 n - 1} \to S^{2 n - 1}$ be a homeomorphism generating a free $ℤ_{p}$ -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 $F : (S^{2 n - 1}, α) \to (X, f_{p})$ . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.

Localization techniques in $L^{p}$ spaces

A. Pełczyński, H. Rosenthal (1975)

Studia Mathematica

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The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure

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 $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.