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

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

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

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.

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.

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.

On décrit un exemple de variété de contact universellement tendue qui devient vrillée après une chirurgie de Dehn admissible sur un entrelacs transverse.

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

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 ${S}^{3}$.

Starting from the work of Bhupal we extend to the contact case the Viterbo capacity and Traynor’s construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.