The connection matrix theory for Morse decompositions

Franzosa, Robert D.

doi:10.1090/S0002-9947-1989-0978368-7

The connection matrix theory for Morse decompositions

Author: Robert D. Franzosa
Journal: Trans. Amer. Math. Soc. 311 (1989), 561-592
MSC: Primary 58F25; Secondary 58E05, 58F09
DOI: https://doi.org/10.1090/S0002-9947-1989-0978368-7
MathSciNet review: 978368
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Abstract: The connection matrix theory for Morse decompositions is introduced. The connection matrices are matrices of maps between the homology indices of the sets in the Morse decomposition. The connection matrices cover, in a natural way, the homology index braid of the Morse decomposition and provide information about the structure of the Morse decomposition. The existence of connection matrices of Morse decompositions is established, and examples illustrating applications of the connection matrix are provided.

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