Relatório de pesquisa 14/08

Spectral sequences in Conley's theory, O. Cornea, K. A. de Rezende, and M. R. da Silveira, submitted Aug. 18.

In this work we present an algorithm for a chain complex C and its differential given by a connection matrix  which determines an associated spectral sequence (E,d). More specifically, a system spanning E in terms of the original basis of C is obtained as well as the identification of all differentials d. In exploring the dynamical implication of a nonzero differential, we prove the existence of a path joining two singularities  in the case that a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow and which proves to be important in some applications.

Mathematics Subject Classifications (2000):  55T05; 37B30; 58F09.

Connection matrix, spectral sequences

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August 18, 2008


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