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Integral formulae for a Riemannian manifold with two orthogonal distributions

Vladimir Rovenski (2011)

Open Mathematics

We obtain a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold, which start from the formula by Walczak (1990) and generalize ones for foliations by several authors. For foliations on space forms our formulae reduce to the classical type formulae by Brito-Langevin-Rosenberg (1981) and Brito-Naveira (2000). The integral formulae involve the conullity tensor of a distribution, and certain components of the...

Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity

Magdalena Zielenkiewicz (2014)

Open Mathematics

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of...

Introduction to the basics of Heegaard Floer homology

Bijan Sahamie (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any prior knowledge of the subject.

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...

Invertible polynomial mappings via Newton non-degeneracy

Ying Chen, Luis Renato G. Dias, Kiyoshi Takeuchi, Mihai Tibăr (2014)

Annales de l’institut Fourier

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

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