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Displaying similar documents to “Representations of the Whitehead manifold W h 3 and Julia sets”

A holomorphic correspondence at the boundary of the Klein combination locus

Shaun Bullett, Andrew Curtis (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We investigate an explicit holomorphic correspondence on the Riemann sphere with striking dynamical behaviour: the limit set is a fractal resembling the one-skeleton of a tetrahedron and on each component of the complement of this set the correspondence behaves like a Fuchsian group.

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.