Displaying similar documents to “Multiple points of singular maps, Part II”

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

Osamu Saeki (1995)

Annales de l'institut Fourier

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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.

Geometric orbifolds.

William D. Dunbar (1988)

Revista Matemática de la Universidad Complutense de Madrid

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An orbifold is a topological space which ?locally looks like? the orbit space of a properly discontinuous group action on a manifold. After a brief review of basic concepts, we consider the special case 3-dimensional orbifolds of the form GammaM, where M is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston?s eight geometries, and where Gamma < Isom(M) acts properly discontinuously. A general description of these geometric orbifolds is given and...