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Constructing generic smooth maps of a manifold into a surface with prescribed singular loci

Osamu Saeki (1995)

Annales de l'institut Fourier

It is known that the singular set S ( f ) of a generic smooth map f : M N of an n -dimensional manifold into a surface is a closed 1-dimensional submanifold of M 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.

Construction of Einstein metrics by generalized Dehn filling

Richard H. Bamler (2012)

Journal of the European Mathematical Society

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.

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 .

Contact topology and the structure of 5-manifolds with π 1 = 2

Hansjörg Geiges, Charles B. Thomas (1998)

Annales de l'institut Fourier

We prove a structure theorem for closed, orientable 5-manifolds M with fundamental group π 1 ( M ) = 2 and second Stiefel-Whitney class equal to zero on H 2 ( M ) . This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain 2 -quotients of  S 2 × S 3 .

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