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

Published electronically:
October 16, 1997

Accompanying material:
Maple program

MathSciNet review:
1472090

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Williams conjecture is false for irreducible subshifts of finite type using relative sign-gyration numbers defined between different subshifts.

**1.**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**, 10.1090/S0894-0347-1992-1130528-4**2.**-,*Williams's conjecture is false for irreducible subshifts*, to appear in Annals of Mathematics.**3.**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**, 10.1090/S0894-0347-1992-1124983-3**4.**Douglas Lind and Brian Marcus,*An introduction to symbolic dynamics and coding*, Cambridge University Press, Cambridge, 1995. MR**1369092****5.**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**0331436**

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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:
http://dx.doi.org/10.1090/S1079-6762-97-00032-2

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