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arXiv · 1311.3520

Generalized Topological Transition Matrix

Robert Franzosa·Ketty A. de Rezende·Ewerton R. Vieira
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Abstract

This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this more general transition matrix satisfies the additional requirement that it covers flow-defined Conley-index isomorphisms, one proves algebraic and connection-existence properties. These general transition matrices with this covering property are referred to as generalized topological transition matrices and are used to consider connecting orbits of Morse-Smale flows without periodic orbits, as well as those in a continuation associated to a dynamical spectral sequence.

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Robert Franzosa, Ketty A. de Rezende, Ewerton R. Vieira. 2013-11-14. Generalized Topological Transition Matrix. https://arxiv.org/abs/1311.3520

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