Linear liftings of skew-symmetric tensor fields to Weil bundles

Jacek Dębecki

Displaying similar documents to “Linear liftings of skew-symmetric tensor fields to Weil bundles”

Degree of T-equivariant maps in ℝⁿ

Joanna Janczewska, Marcin Styborski (2007)

Banach Center Publications

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A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution $T : ℝ^{p} \oplus ℝ^{q} \to ℝ^{p} \oplus ℝ^{q}$ given by T(u,v) = (u,-v). The presented construction is self-contained. It is also shown that two T-equivariant gradient maps $f, g : (ℝ ⁿ, S^{n - 1}) \to (ℝ ⁿ, ℝ ⁿ ∖ 0)$ are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.

An $S^{1}$ -equivariant degree and the Fuller index

Grzegorz Dylawerski, Kazimierz Gęba, Jerzy Jodel, Wacław Marzantowicz (1991)

Annales Polonici Mathematici

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On applications of the Yano–Ako operator

A. Magden, Arif A. Salimov (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we consider a method by which a skew-symmetric tensor field of type (1,2) in $M_{n}$ can be extended to the tensor bundle $T_{q}^{0} (M_{n})$ $(q > 0)$ on the The results obtained are to some extend similar to results previously established for cotangent bundles $T_{1}^{0} (M_{n})$ . However, there are various important differences and it appears that the problem of lifting tensor fields of type (1,2) to the tensor bundle $T_{q}^{0} (M_{n})$ $(q > 1)$ on the presents difficulties which are not encountered in the...

On torsion of a $3$ -web

Alena Vanžurová (1995)

Mathematica Bohemica

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A 3-web on a smooth $2 n$ -dimensional manifold can be regarded locally as a triple of integrable $n$ -distributions which are pairwise complementary, [5]; that is, we can work on the tangent bundle only. This approach enables us to describe a $3$ -web and its properties by invariant $(1, 1)$ -tensor fields $P$ and $B$ where $P$ is a projector and $B^{2} =$ id. The canonical Chern connection of a web-manifold can be introduced using this tensor fields, [1]. Our aim is to express the torsion tensor $T$ of the Chern connection...

Equivariant deformation quantization for the cotangent bundle of a flag manifold

Ranee Brylinski (2002)

Annales de l’institut Fourier

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Let $X$ be a (generalized) flag manifold of a complex semisimple Lie group $G$ . We investigate the problem of constructing a graded star product on $ℛ = R (T^{☆} X)$ which corresponds to a $G$ -equivariant quantization of symbols into twisted differential operators acting on half-forms on $X$ . We construct, when $ℛ$ is generated by the momentum functions $μ^{x}$ for $G$ , a preferred choice of $☆$ where $μ^{x} ☆ φ$ has the form $μ^{x} φ + \frac{1}{2} {μ^{x}, φ} t + Λ^{x} (φ) t^{2}$ . Here $Λ^{x}$ are operators on $ℛ$ . In the known examples, $Λ^{x}$ ( $x \neq 0$ ) is not a differential operator, and so the star...

Positivity and Kleiman transversality in equivariant $K$ -theory of homogeneous spaces

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 $K$ -theory of generalized ﬂag varieties $G / P$ . 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...

Equivariant measurable liftings

Nicolas Monod (2015)

Fundamenta Mathematicae

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We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to $L^{\infty}$ -cocycles for characteristic classes.

Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Josef Janyška (2001)

Archivum Mathematicum

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Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$ . We classify all natural (in the sense of [KMS]) 0-order vector fields and 2-vector fields on $T M$ generated by $g$ and $K$ . We get that all natural vector fields are of the form $E (u) = α (h (u)) u^{H} + β (h (u)) u^{V},$ where $u^{V}$ is the vertical lift of $u \in T_{x} M$ , $u^{H}$ is the horizontal lift of $u$ with respect to $K$ , $h (u) = 1 / 2 g (u, u)$ and $α, β$ are smooth real functions defined on $R$ . All natural 2-vector fields are of the form $Λ (u) = γ_{1} (h (u)) Λ (g, K) + γ_{2} (h (u)) u^{H} \land u^{V},$ where $γ_{1}$ , $γ_{2}$ are smooth real functions...