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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
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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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