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We show that if is a discrete subgroup of the group of the isometries of , and if is a representation of into the group of the isometries of , then any -equivariant map extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable -equivariant...
It is known that the singular set of a generic smooth map of an -dimensional manifold into a surface is a closed 1-dimensional submanifold of and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characterization of those 1-dimensional (stratified) submanifolds which arise as the singular set of a generic map in terms of the homology class they represent.
We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold . The main theorem says that there is a unique obstruction element in , where is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and is compact, we obtain a PL-manifold which is simple homotopy equivalent to .
In this paper, we present a new approach to the construction of Einstein metrics by a generalization of Thurston's Dehn filling. In particular in dimension 3, we will obtain an analytic proof of Thurston's result.
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 . Together with the earlier classification of overtwisted contact structures on 3-manifolds this result completes the classification of contact structures on .
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.
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