Markov partitions and

J. B. Wagoner

Publications Mathématiques de l'IHÉS (1987)

  • Volume: 65, page 91-129
  • ISSN: 0073-8301

How to cite

top

Wagoner, J. B.. "Markov partitions and $K_2$." Publications Mathématiques de l'IHÉS 65 (1987): 91-129. <http://eudml.org/doc/104023>.

@article{Wagoner1987,
author = {Wagoner, J. B.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {subshift of finite type; uniform Markov partitions; dimension group; algebraic K-theory group; fundamental group; shift equivalences; category of nonnegative integral matrices},
language = {eng},
pages = {91-129},
publisher = {Institut des Hautes Études Scientifiques},
title = {Markov partitions and $K_2$},
url = {http://eudml.org/doc/104023},
volume = {65},
year = {1987},
}

TY - JOUR
AU - Wagoner, J. B.
TI - Markov partitions and $K_2$
JO - Publications Mathématiques de l'IHÉS
PY - 1987
PB - Institut des Hautes Études Scientifiques
VL - 65
SP - 91
EP - 129
LA - eng
KW - subshift of finite type; uniform Markov partitions; dimension group; algebraic K-theory group; fundamental group; shift equivalences; category of nonnegative integral matrices
UR - http://eudml.org/doc/104023
ER -

References

top
  1. [B] H. BASS, Algebraic K-Theory, W. A. Benjamin, 1968. Zbl0174.30302MR40 #2736
  2. [BF] R. BOWEN and J. FRANKS, Homology for zero-dimensional non-wandering sets, Ann. of Math., 106 (1977), 73-92. Zbl0375.58018MR56 #16692
  3. [BK] M. BOYLE and W. KRIEGER, Periodic points and automorphisms of the shift, to appear in Trans. Amer. Math. Soc. Zbl0621.58031
  4. [BLR] M. BOYLE, D. LIND and D. RUDOLPH, The automorphism group of a subshift of finite type, preprint, University of Washington / University of Maryland (1986). Zbl0664.28006
  5. [C] A. CONNES, Outer conjugacy of classes of automorphisms of factors, Ann. Sci. Ec. Norm. Sup., 4e série, 8 (1975), 383-420. Zbl0342.46052MR52 #15031
  6. [CS] A. CONNES and E. STÖRMER, Entropy for automorphisms of II1 von Neumann algebras, Acta Mathematica, 134 (1975), 289-306. Zbl0326.46032
  7. [Cu1] J. CUNTZ, A class of C*-algebras and topological Markov chains, II : Reducible chains and the Ext-functor for C*-algebras, Invent. Math., 63 (1981), 25-40. Zbl0461.46047MR82f:46073b
  8. [Cu2] J. CUNTZ, On the homotopy groups of the space of endomorphisms of a C*-algebra (with applications to topological Markov chains), in Operator Algebras and Group Representations, Vols. 1 and 2, Monographs and Studies in Mathematics, Nos. 17 and 18, Conference at Neptun, Romania, 1980, pp. 124-137. Zbl0561.46025
  9. [CK] J. CUNTZ and W. KRIEGER, A class of C*-algebras and topological Markov chains, Invent. Math., 56 (1980), 251-268. Zbl0434.46045MR82f:46073a
  10. [E] E. G. EFFROS, Dimensions and C*-algebras, CBMS, no. 46 (American Mathematical Society, 1981). Zbl0475.46050MR84k:46042
  11. [F] J. FRANKS, Homology and dynamical systems, CBMS, no. 49 (American Mathematical Society, 1982). Zbl0497.58018MR84f:58067
  12. [H] G. HEDLUND, Endomorphisms and automorphisms of the shift dynamical system, Mathematical Systems Theory, 3, no. 4 (1969), 320-375. Zbl0182.56901MR41 #4510
  13. [HW] A. HATCHER and J. WAGONER, Pseudo-isotopies of compact manifolds, Astérisque, 6, Société Mathématique de France (1973). Zbl0274.57010MR50 #5821
  14. [K] W. KRIEGER, On dimension functions and topological Markov chains, Invent. Math., 56 (1980), 239-250. Zbl0431.54024MR81m:28018
  15. [KV] V. A. KAIMANOVICH and A. M. VERSHIK, Random walks on discrete groups : boundary and entropy, Annals of Probability, 11, no. 3 (1983), 457-490. Zbl0641.60009MR85d:60024
  16. [M1] J. MILNOR, Introduction to Algebraic K-theory, Annals of Math. Studies No. 72, Princeton University Press, 1971. Zbl0237.18005MR50 #2304
  17. [M2] J. MILNOR, Infinite cyclic coverings, Conference on Topology of Manifolds, ed. J. G. HOCKING, Vol. 13, Prindle, Weber & Schmidt, Inc., 1968, 115-133. Zbl0179.52302MR39 #3497
  18. [M3] J. MILNOR, Whitehead torsion, BAMS, 72 (1966), 358-426. Zbl0147.23104MR33 #4922
  19. [PT] W. PARRY and S. TUNGEL, Classification Problems in Ergodic Theory, LMS Lecture Notes, 67, Cambridge University Press, 1982. Zbl0487.28014MR84g:28024
  20. [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. Zbl0383.94011MR57 #6368
  21. [Q] D. QUILLEN, Higher algebraic K-theory, I, Springer Lecture Notes in Mathematics, No. 341 (1973), 85-147. Zbl0292.18004MR49 #2895
  22. [S] G. SEGAL, Classifying spaces and spectral sequences, Publ. Math., I.H.E.S., 34 (1968), 105-112. Zbl0199.26404MR38 #718
  23. [Sp] E. SPANIER, Algebraic Topology, McGraw-Hill, 1966. Zbl0145.43303MR35 #1007
  24. [T] S. TUNCEL, A dimension, dimension modules, and Markov chains, Proc. London Math. Soc., 36 (1983), 100-116. Zbl0544.28011MR84m:28032
  25. [W1] J. WAGONER, K2 and diffeomorphisms of two and three dimensional manifolds, Geometric Topology, ed. J. C. CANTRELL, Academic Press, 1979, 557-580. Zbl0493.57013MR80h:57043
  26. [W2] J. WAGONER, Topological Markov chains, C*-algebras, and K2, preprint, to appear in Advances in Mathematics. Zbl0664.46068
  27. [Wi] R. F. WILLIAMS, Classification of subshifts of finite type, Ann. of Math., 98 (1973), 120-153 ; Errata, ibid., 99 (1974), 380-381. Zbl0282.58008MR48 #9769
  28. [Z] F. ZIZZA, Automorphisms of hyperbolic dynamical systems and K2, Ph.D. Thesis, University of California, Berkeley (1985). Also a preprint from University of Washington, Seattle. Zbl0672.34065

NotesEmbed ?

top

You must be logged in to post comments.