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J. Math. Kyoto Univ. (JMKYAZ) Equivalence of Graded Module Braids

Summary: J. Math. Kyoto Univ. (JMKYAZ)
Equivalence of Graded Module Braids
and Interlocking Sequences
The category of totally ordered graded module braids and that of
the exact interlocking sequences are shown to be equivalent. As an appli-
cation of this equivalence, we show the existence of a connection matrix
for a totally ordered graded module braid without assuming the existence
of chain complex braid that induces the given graded module braid.
1. Introduction
The connection matrix theory has been an useful tool for topological stud-
ies of dynamical systems [2, 3]. When an isolated invariant set of a dynamical
system admits a Morse decomposition, a connection matrix for the decompo-
sition describes the relation of the homological Conley index of the isolated
invariant set and that of the isolated invariant subsets. This provides informa-
tion about the structure of connecting orbits, and furthermore, the difference
of the connection matrices between distinct parameter values often provides


Source: Arai, Zin - Department of Mathematics, Kyoto University


Collections: Mathematics