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$𝒞^{0}$ -rigidity of characteristics in symplectic geometry

Emmanuel Opshtein (2009)

Annales scientifiques de l'École Normale Supérieure

The paper concerns a $𝒞^{0}$ -rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.

$1$ -cocycles on the group of contactomorphisms on the supercircle $S^{1 | 3}$ generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

The relative cohomology $H_{diff}^{1} (𝕂 (1 | 3), 𝔬𝔰𝔭 (2, 3); 𝒟_{λ, μ} (S^{1 | 3}))$ of the contact Lie superalgebra $𝕂 (1 | 3)$ with coefficients in the space of differential operators $𝒟_{λ, μ} (S^{1 | 3})$ acting on tensor densities on $S^{1 | 3}$ , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating $1$ -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative $1$ -cocycle $s (X_{f}) = D_{1} D_{2} D_{3} (f) α_{3}^{1 / 2}$ , $X_{f} \in 𝕂 (1 | 3)$ which is invariant with respect to the conformal subsuperalgebra $𝔬𝔰𝔭 (2, 3)$ of $𝕂 (1 | 3)$ . In this work we study the supergroup case. We give an explicit construction of $1$ -cocycles of the group...

2- II Inégalités fortes de Morse

E. Combet (1984)

Publications du Département de mathématiques (Lyon)

2 Inégalités de Morse d'après E. Witten

E. Combet (1984)

Publications du Département de mathématiques (Lyon)

3 Classification des plongements isotropes d'après A. Weinstein

D. Sondaz (1983)

Publications du Département de mathématiques (Lyon)

4-dimensional c-symplectic $S^{1}$ -manifolds with non-empty fixed point set need not be c-Hamiltonian

Akio Hattori (1998)

Banach Center Publications

The aim of this article is to answer a question posed by J. Oprea in his talk at the Workshop "Homotopy and Geometry".

$𝔤$ -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

A Lie version of Turaev’s $\bar{G}$ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a $𝔤$ -quasi-Frobenius Lie algebra for $𝔤$ a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra $(𝔮, β)$ together with a left $𝔤$ -module structure which acts on $𝔮$ via derivations and for which $β$ is $𝔤$ -invariant. Geometrically, $𝔤$ -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...