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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0978368-7

Keywords:
Conley index,
Morse decomposition,
connection matrix

Article copyright:
© Copyright 1989
American Mathematical Society