Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Automorphisms of the dimension group and gyration numbers


Authors: K. H. Kim, F. W. Roush and J. B. Wagoner
Journal: J. Amer. Math. Soc. 5 (1992), 191-212
MSC: Primary 54H20; Secondary 20F28, 28D99, 58F03
DOI: https://doi.org/10.1090/S0894-0347-1992-1124983-3
MathSciNet review: 1124983
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [B] K. Baker, Strong shift equivalence of 2 by 2 matrices of non negative integers, Ergodic Theory Dynamical Systems 3 (1983), 501-508. MR 753918 (86g:28021)
  • [BH] M. Boyle and D. Handelman, Algebraic shift equivalence and primitive matrices, preprint, Univ. of Maryland 1990. MR 1102219 (93e:58050)
  • [BK] M. Boyle and W. Krieger, Periodic points and automorphisms of the shift, Trans. Amer. Math. Soc. 302 (1987), 125-149. MR 887501 (88g:54065)
  • [BLR] M. Boyle, D. Lind, and D. Rudolph, The automorphism group of a shift of finite type, Trans. Amer. Math. Soc. 306 (1988), 71-114. MR 927684 (89m:54051)
  • [CK] J. Cuntz and W. Krieger, Topological Markov chains and dicyclic dimension groups, J. Reine Angew. Math. 320 (1980), 44-51. MR 592141 (81m:54074)
  • [DGS] M. Denker, C. Grillenberger, and K. Sigmund, Ergodic theory on compact spaces, Lecture Notes in Math, vol. 527, Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0457675 (56:15879)
  • [E] E. Effros, Dimensions and $ {C^ * }$-algebras, CBMS, No. 46, Amer. Math. Soc., Providence, RI, 1981. MR 623762 (84k:46042)
  • [F1] U. Fiebig, Uber gyrationszahlenfolgen und ein darstellungenproblem in der symbolischen dynamik, Dissertation, Univ. of Gottingen, 1987.
  • [F2] -, Gyration numbers for involutions of subshifts of finite type, Math. Forum (to appear).
  • [Fr] J. Franks, Homology and dynamical systems, CBMS No. 49, Amer. Math. Soc., Providence, RI, 1982. MR 669378 (84f:58067)
  • [H] D. Handelman, Positive matrices and dimension groups, J. Operator Theory 6 (1981), 55-74. MR 637001 (84i:46058)
  • [He] G. Hedlund, Endomorphisms and automorphisms of shift dynamical systems, Math. Systems Theory 3 (1969), 320-375. MR 0259881 (41:4510)
  • [K] W. Krieger, On dimension functions and topological Markov chains, Invent. Math. 56 (1980), 239-250. MR 561973 (81m:28018)
  • [KR1] H. Kim and F. W. Roush, Some results on decidability of shift equivalence, J. Combin. Inform. System Sci. 4 (1979), 123-146. MR 564188 (81m:58064)
  • [KR2] -, On the structure of inert automorphisms of subshifts, preprint, Alabama State Univ. at Montgomery 1989.
  • [KR3] -, Williams's conjecture is false for reducible subshifts, J. Amer. Math. Soc. 5 (1992), 213-215 (this issue). MR 1130528 (92j:54055)
  • [N] M. Nasu, Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markovc chaings, Dynamical Systems, Lecture Notes in Math., vol. 1342, Springer-Verlag, Berlin-Heidelberg-New York, 1988, pp. 564-607. MR 970572 (89j:54045)
  • [PT] W. Parry and S. Tuncel, Classification problems in ergodic theory, LMS Lecture Notes, No. 67, Cambridge Univ. Press, 1982. MR 666871 (84g:28024)
  • [PW] W. Parry and R. F. Williams, Block coding and a zeta function for finite Markov chains, Proc. London Math. Soc. (3) 35 (1977), 483-495. MR 0466490 (57:6368)
  • [W1] J. Wagoner, Markov partitions and $ {K_2}$ , Publ. Math. IHES, no. 65, 1987. MR 908217 (90d:28022)
  • [W2] -, Triangle Identities and symmetries of a subshift of finite type, Pacific J. Math. 144 (1990), 181-205. MR 1056673 (91h:28017)
  • [W3] -, Eventual finite order generation for the kernel of the dimension group representation, Trans. Amer. Math. Soc. 317 (1990), 331-350. MR 1027363 (91a:54055)
  • [W4] -, Higher dimensional shift equivalence is the same as strong shift equivalence over the integers, Proc. Amer. Math. Soc. 109 (1990), 527-536. MR 1012941 (90i:54088)
  • [We] E. Weiss, Algebraic number theory, McGraw-Hill, New York, 1963. MR 0159805 (28:3021)
  • [Wi1] R. F. Williams, Classification of one-dimensional attractors, Proc. Sympos. Pure Math. vol. 14, Amer. Math. Soc., Providence, RI, 1970, pp. 341-361. MR 0266227 (42:1134)
  • [Wi2] -, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120-153; Errata ibid. 99 (1974), 380-381. MR 0331436 (48:9769)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 54H20, 20F28, 28D99, 58F03

Retrieve articles in all journals with MSC: 54H20, 20F28, 28D99, 58F03


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1992-1124983-3
Keywords: Sign-gyration-compatibility-condition homomorphism
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society