Eventual finite order generation for the kernel of the dimension group representation

Author:
J. B. Wagoner

Journal:
Trans. Amer. Math. Soc. **317** (1990), 331-350

MSC:
Primary 54H20; Secondary 57S99, 60J10

DOI:
https://doi.org/10.1090/S0002-9947-1990-1027363-9

MathSciNet review:
1027363

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Abstract | References | Similar Articles | Additional Information

Abstract: The finite order generation problem (FOG) in symbolic dynamics asks whether every element in the kernel of the dimension group representation of a subshift of finite type is a product of elements of finite order in the group of homeomorphisms of commuting with . We study the space of strong shift equivalences over the nonnegative integers, and the first application is to prove Eventual FOG which says that every inert symmetry of is a product of finite order homeomorphisms of commuting with sufficiently high powers of . Then we discuss the relation of FOG to Williams' lifting problem (LIFT) for symmetries of fixed points. In particular, either FOG or LIFT is false. Finally, we also discuss -adic convergence and other implications of Eventual FOG for gyration numbers.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-1027363-9

Keywords:
Kernel of the dimension group representation,
Eventual FOG,
the space of strong shift equivalences,
LIFT,
-adic asymptotic gyration numbers

Article copyright:
© Copyright 1990
American Mathematical Society