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Currently published by the American Institute of Mathematical Sciences as Electronic Research Announcements in Mathematical Sciences

The Williams conjecture is false for irreducible subshifts

Author(s): K. H. Kim; F. W. Roush
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 105-109.
MSC (1991): Primary 58F03, 54H20
Posted: October 16, 1997
Accompanying material: Maple program
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Abstract: We prove that the Williams conjecture is false for irreducible subshifts of finite type using relative sign-gyration numbers defined between different subshifts.

References:

1.: K. H. Kim and F. W. Roush, Williams's conjecture is false for reducible subshifts, J. Amer. Math. Soc. 5 (1992), 213-215. MR 92j:54055
2.: -, Williams's conjecture is false for irreducible subshifts, to appear in Annals of Mathematics.
3.: K. H. Kim, F. W. Roush, and J. Wagoner, Automorphisms of the dimension group and gyration numbers, J. Amer. Math. Soc. 5 (1992), 191-212. MR 93h:54026
4.: D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, 1995. MR 97a:58050
5.: R. F. Williams, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120-153; Errata ibid. 99 (1974), 380-381. MR 48:9769

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Additional Information:

K. H. Kim
Affiliation: Mathematics Research Group, Alabama State University, Montgomery, AL 36101-0271, and Korean Academy of Science and Technology
Email: kkim@asu.alasu.edu

F. W. Roush
Affiliation: Mathematics Research Group, Alabama State University, Montgomery, AL 36101-0271
Email: froush@asu.alasu.edu

DOI: 10.1090/S1079-6762-97-00032-2
PII: S 1079-6762(97)00032-2
Keywords: Williams conjecture, irreducible subshift of finite type, strong shift equivalence, gyration numbers
Received by editor(s): June 5, 1997
Posted: October 16, 1997
Additional Notes: The authors were partially supported by NSF Grants DMS 9024813 and DMS 9405004.
Communicated by: Svetlana Katok
Copyright of article: Copyright 1997, American Mathematical Society


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