Displaying similar documents to “Morse-Bott functions with two critical values on a surface”

Pruning theory and Thurston's classification of surface homeomorphisms

André de Carvalho, Toby Hall (2001)

Journal of the European Mathematical Society

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Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading – both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy.

Generalized matrix graphs and completely independent critical cliques in any dimension

John J. Lattanzio, Quan Zheng (2012)

Discussiones Mathematicae Graph Theory

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For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product Iₙ × Iₙ × ... × Iₙ. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is investigated. It is shown that there exists a vertex critical graph which admits a family of k...

On surface braids of index four with at most two crossings

Teruo Nagase, Akiko Shima (2005)

Fundamenta Mathematicae

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Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.