Index filtrations and the homology index braid for partially ordered Morse decompositions

Author:
Robert Franzosa

Journal:
Trans. Amer. Math. Soc. **298** (1986), 193-213

MSC:
Primary 58F12; Secondary 58E05, 58F25

DOI:
https://doi.org/10.1090/S0002-9947-1986-0857439-7

MathSciNet review:
857439

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Abstract: On a Morse decomposition of an invariant set in a flow there are partial orderings defined by the flow. These are called admissible orderings of the Morse decomposition. The index filtrations for a total ordering of a Morse decomposition are generalized in this paper with the definition and proof of existence of index filtrations for admissible partial orderings of a Morse decomposition.

It is shown that associated to an index filtration there is a collection of chain complexes and chain maps called the chain complex braid of the index filtration. The homology index braid of the corresponding admissible ordering of the Morse decomposition is obtained by passing to homology in the chain complex braid.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0857439-7

Keywords:
Morse decomposition,
Conley index,
index filtration

Article copyright:
© Copyright 1986
American Mathematical Society