Eventual finite order generation for the kernel of the dimension group representation
Author:
J. B. Wagoner
Journal:
Trans. Amer. Math. Soc. 317 (1990), 331350
MSC:
Primary 54H20; Secondary 57S99, 60J10
MathSciNet review:
1027363
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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:
http://dx.doi.org/10.1090/S00029947199010273639
PII:
S 00029947(1990)10273639
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
