All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 43

Showing per page

Rational BV-algebra in string topology

Yves Félix, Jean-Claude Thomas (2008)

Bulletin de la Société Mathématique de France

Let M be a 1-connected closed manifold of dimension m and L M be the space of free loops on M . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of L M , H * ( L M ; k ) . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology H H * ( C * ( M ) ; C * ( M ) ) which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between H H * ( C * ( M ) ; C * ( M ) ) and the shifted homology H * + m ( L M ; k ) . We also prove that the...

Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

H. Shiga, M. Tezuka (1987)

Annales de l'institut Fourier

We show that an orientable fibration whose fiber has a homotopy type of homogeneous space G / U with rank G = rang U is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of G plays a key role in the proof. We also show that it is valid for mod. p coefficients if p does not divide the order of the Weyl group of G .

Rational homotopy of Serre fibrations

Jean-Claude Thomas (1981)

Annales de l'institut Fourier

In rational homotopy theory, we show how the homotopy notion of pure fibration arises in a natural way. It can be proved that some fibrations, with homogeneous spaces as fibre are pure fibrations. Consequences of these results on the operation of a Lie group and the existence of Serre fibrations are given. We also examine various measures of rational triviality for a fibration and compare them with and whithout the hypothesis of pure fibration.

Rational models of solvmanifolds with Kählerian structures.

A. Tralle (1997)

Revista Matemática de la Universidad Complutense de Madrid

We investigate the existence of symplectic non-Kählerian structures on compact solvmanifolds and prove some results which give strong necessary conditions for the existence of Kählerian structures in terms of rational homotopy theory. Our results explain known examples and generalize the Benson-Gordon theorem (Benson and Gordon (1990); our method allows us to drop the assumption of the complete solvability of G).

Rational string topology

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2007)

Journal of the European Mathematical Society

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold M . We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the cochain algebra C * ( M ) with coefficients in C * ( M ) . Some explicit computations of the loop product and the string bracket are given.

Currently displaying 1 – 20 of 43

Page 1 Next