The Williams conjecture is false for irreducible subshifts
Authors:
K. H. Kim and F. W. Roush
Journal:
Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 105-109
MSC (1991):
Primary 58F03, 54H20
DOI:
https://doi.org/10.1090/S1079-6762-97-00032-2
Published electronically:
October 16, 1997
Accompanying material:
Maple program
MathSciNet review:
1472090
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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.
- K. H. Kim and F. W. Roush, Williams’s conjecture is false for reducible subshifts, J. Amer. Math. Soc. 5 (1992), no. 1, 213–215. MR 1130528, DOI 10.1090/S0894-0347-1992-1130528-4
- —, Williams’s conjecture is false for irreducible subshifts, to appear in Annals of Mathematics.
- K. H. Kim, F. W. Roush, and J. B. Wagoner, Automorphisms of the dimension group and gyration numbers, J. Amer. Math. Soc. 5 (1992), no. 1, 191–212. MR 1124983, DOI 10.1090/S0894-0347-1992-1124983-3
- Douglas Lind and Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge, 1995. MR 1369092, DOI 10.1017/CBO9780511626302
- R. F. Williams, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120–153; errata, ibid. (2) 99 (1974), 380–381. MR 331436, DOI 10.2307/1970908
- K. H. Kim and F. W. Roush, Williams’s conjecture is false for reducible subshifts, J. Amer. Math. Soc. 5 (1992), 213–215.
- —, Williams’s conjecture is false for irreducible subshifts, to appear in Annals of Mathematics.
- 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.
- D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, 1995.
- R. F. Williams, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120–153; Errata ibid. 99 (1974), 380–381.
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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
Keywords:
Williams conjecture,
irreducible subshift of finite type,
strong shift equivalence,
gyration numbers
Received by editor(s):
June 5, 1997
Published electronically:
October 16, 1997
Additional Notes:
The authors were partially supported by NSF Grants DMS 9024813 and DMS 9405004.
Communicated by:
Svetlana Katok
Article copyright:
© Copyright 1997
American Mathematical Society
