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A quantum Duistermaat-Heckamn formula?

Alberto Ibort (2003)


Some aspects of Duistermaat-Heckman formula in finite dimensions are reviewed. We especulate with some of its possible extensions to infinite dimensions. In particular we review the localization principle and the geometry of loop spaces following Witten and Atiyah?s insight.

A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds

Stefan Friedl, Stefano Vidussi (2013)

Journal of the European Mathematical Society

In this paper we show that given any 3-manifold N and any non-fibered class in H 1 ( N ; Z ) there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.

An invariant of nonpositively curved contact manifolds

Thilo Kuessner (2011)

Open Mathematics

We define an invariant of contact structures and foliations (on Riemannian manifolds of nonpositive sectional curvature) which is upper semi-continuous with respect to deformations and thus gives an obstruction to the topology of foliations which can be approximated by isotopies of a given contact structure.

Codimension one symplectic foliations.

Omegar Calvo, Vicente Muñoz, Francisco Presas (2005)

Revista Matemática Iberoamericana

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

Contact 3-manifolds twenty years since J. Martinet's work

Yakov Eliashberg (1992)

Annales de l'institut Fourier

The paper gives an account of the recent development in 3-dimensional contact geometry. The central result of the paper states that there exists a unique tight contact structure on S 3 . Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on S 3 .

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