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Invariants homotopiques attachés aux fibrés symplectiques

Pierre Dazord (1979)

Annales de l'institut Fourier

On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne 2 q -orientée dans R n ⊕ R n * : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré q -symplectique, c’est-à-dire dont le groupe structural est le revêtement à q feuillets de S p ( n ) . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...

Invariants of analytic curves.

Hans J. Zwiesler (1989)

Publicacions Matemàtiques

In this article we introduce a complete system of geometric invariants for an analytic curve. No restrictions are imposed on the curve and the invariants can be easily computed.

Invariants of complex structures on nilmanifolds

Edwin Alejandro Rodríguez Valencia (2015)

Archivum Mathematicum

Let ( N , J ) be a simply connected 2 n -dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on N compatible with J to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving...

Invariants of real symplectic four-manifolds out of reducible and cuspidal curves

Jean-Yves Welschinger (2006)

Bulletin de la Société Mathématique de France

We construct invariants under deformation of real symplectic four-manifolds. These invariants are obtained by counting three different kinds of real rational J -holomorphic curves which realize a given homology class and pass through a given real configuration of (the appropriate number of) points. These curves are cuspidal curves, reducible curves and curves with a prescribed tangent line at some real point of the configuration. They are counted with respect to some sign defined by the parity of...

Invariants symplectiques et semi-classiques des systèmes intégrables avec singularités

San Vũ Ngọc (2000/2001)

Séminaire Équations aux dérivées partielles

On définit les notions de feuilletages classiques et semi-classiques pour les systèmes complètement intégrables avec singularités. Les résultats de classification standard (telles les coordonnées actions-angles semi-classiques) sont rappelés. Le cas du feuilletage classique de type foyer-foyer est examiné en détail, où des nouveaux invariants semi-globaux apparaissent. Ces invariants sont identifiés dans les conditions de Bohr-Sommerfeld singulières qui donnent le spectre conjoint au voisinage d’une...

Invertible Carnot Groups

David M. Freeman (2014)

Analysis and Geometry in Metric Spaces

We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.

Isometric Embeddings of Pro-Euclidean Spaces

Barry Minemyer (2015)

Analysis and Geometry in Metric Spaces

In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...

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