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A footnote on expanding maps
K-groups of the full group actions on one-sided topological Markov shifts
1. | Department of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan |
References:
[1] |
M. Boyle, "Topological Orbit Equivalence and Factor Maps in Symbolic Dynamics," Ph.D. thesis, University of Washington, 1983. |
[2] |
M. Boyle and D. Handelman, Orbit equivalence, flow equivalence and ordered cohomology, Israel J. Math., 95 (1996), 169-210.
doi: 10.1007/BF02761039. |
[3] |
M. D. Choi, A simple $C^*$-algebras generated by two finite order unitaries, Canad. J. Math., 31 (1979), 867-880.
doi: 10.4153/CJM-1979-082-4. |
[4] |
J. Cuntz, Simple $C^*$-algebras generated by isometries, Comm. Math. Phys., 57 (1977), 173-185. |
[5] |
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.
doi: 10.1007/BF01389192. |
[6] |
J. Cuntz, K-theory for certain $C^*$-algebras, Ann. Math. (2), 113 (1981), 181-197.
doi: 10.2307/1971137. |
[7] |
J. Cuntz and W. Krieger, A class of $C^*$-algebras and topological Markov chains, Invent. Math., 56 (1980), 251-268.
doi: 10.1007/BF01390048. |
[8] |
T. Giordano, I. F. Putnam and C. F. Skau, Topological orbit equivalence and $C^*$-crossed products, J. Reine Angew. Math., 469 (1995), 51-111. |
[9] |
T. Giordano, I. F. Putnam and C. F. Skau, Full groups of Cantor minimal systems, Israel J. Math., 111 (1999), 285-320.
doi: 10.1007/BF02810689. |
[10] |
T. Giordano, H. Matui, I. F. Putnam and C. F. Skau, Orbit equivalence for Cantor minimal $\mathbb Z^d$-systems, Invent. Math., 179 (2010), 119-158.
doi: 10.1007/s00222-009-0213-7. |
[11] |
R. H. Herman, I. F. Putnam and C. F. Skau, Ordered Bratteli diagrams, dimension groups and topological dynamics, Internat. J. Math., 3 (1992), 827-864.
doi: 10.1142/S0129167X92000382. |
[12] |
W. Magnus, A. Karrass and D. Solitar, "Combinatorial Group Theory. Presentations of groups in terms of generators and relations," Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. |
[13] |
K. Matsumoto, On automorphisms of $C^*$-algebras associated with subshifts, J. Operator Theory, 44 (2000), 91-112. |
[14] |
K. Matsumoto, Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras, Pacific J. Math., 246 (2010), 199-225.
doi: 10.2140/pjm.2010.246.199. |
[15] |
K. Matsumoto, Classification of Cuntz-Krieger algebras by orbit equivalence of topological Markov shifts, to appear in Proc. Amer. Math. Soc. |
[16] |
K. Matsumoto, Full groups of one-sided topological Markov shifts, preprint, arXiv:1205.1320. |
[17] |
H. Matui, Homology and topological full groups of étale groupoids on totally disconnected spaces, Proc. London Math. Soc. (3), 104 (2012), 27-56.
doi: 10.1112/plms/pdr029. |
[18] |
I. F. Putnam, The $C^*$-algebras associated with minimal homeomorphisms of the Cantor set, Pacific J. Math., 136 (1989), 329-353. |
[19] |
M. Rφrdam, Classification of Cuntz-Krieger algebras, K-theory, 9 (1995), 31-58.
doi: 10.1007/BF00965458. |
[20] |
M. Rφrdam, F. Larsen and N. J. Laustsen, "An Introduction to K-Theory for $C^*$-Algebras," London Mathematical Society Student Texts, 49, Cambridge University Press, Cambridge, 2000. |
[21] |
J. Spielberg, Free-product groups, Cuntz-Krieger algebras, and covariant maps, Internat. J. Math., 2 (1991), 457-476.
doi: 10.1142/S0129167X91000260. |
show all references
References:
[1] |
M. Boyle, "Topological Orbit Equivalence and Factor Maps in Symbolic Dynamics," Ph.D. thesis, University of Washington, 1983. |
[2] |
M. Boyle and D. Handelman, Orbit equivalence, flow equivalence and ordered cohomology, Israel J. Math., 95 (1996), 169-210.
doi: 10.1007/BF02761039. |
[3] |
M. D. Choi, A simple $C^*$-algebras generated by two finite order unitaries, Canad. J. Math., 31 (1979), 867-880.
doi: 10.4153/CJM-1979-082-4. |
[4] |
J. Cuntz, Simple $C^*$-algebras generated by isometries, Comm. Math. Phys., 57 (1977), 173-185. |
[5] |
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.
doi: 10.1007/BF01389192. |
[6] |
J. Cuntz, K-theory for certain $C^*$-algebras, Ann. Math. (2), 113 (1981), 181-197.
doi: 10.2307/1971137. |
[7] |
J. Cuntz and W. Krieger, A class of $C^*$-algebras and topological Markov chains, Invent. Math., 56 (1980), 251-268.
doi: 10.1007/BF01390048. |
[8] |
T. Giordano, I. F. Putnam and C. F. Skau, Topological orbit equivalence and $C^*$-crossed products, J. Reine Angew. Math., 469 (1995), 51-111. |
[9] |
T. Giordano, I. F. Putnam and C. F. Skau, Full groups of Cantor minimal systems, Israel J. Math., 111 (1999), 285-320.
doi: 10.1007/BF02810689. |
[10] |
T. Giordano, H. Matui, I. F. Putnam and C. F. Skau, Orbit equivalence for Cantor minimal $\mathbb Z^d$-systems, Invent. Math., 179 (2010), 119-158.
doi: 10.1007/s00222-009-0213-7. |
[11] |
R. H. Herman, I. F. Putnam and C. F. Skau, Ordered Bratteli diagrams, dimension groups and topological dynamics, Internat. J. Math., 3 (1992), 827-864.
doi: 10.1142/S0129167X92000382. |
[12] |
W. Magnus, A. Karrass and D. Solitar, "Combinatorial Group Theory. Presentations of groups in terms of generators and relations," Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. |
[13] |
K. Matsumoto, On automorphisms of $C^*$-algebras associated with subshifts, J. Operator Theory, 44 (2000), 91-112. |
[14] |
K. Matsumoto, Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras, Pacific J. Math., 246 (2010), 199-225.
doi: 10.2140/pjm.2010.246.199. |
[15] |
K. Matsumoto, Classification of Cuntz-Krieger algebras by orbit equivalence of topological Markov shifts, to appear in Proc. Amer. Math. Soc. |
[16] |
K. Matsumoto, Full groups of one-sided topological Markov shifts, preprint, arXiv:1205.1320. |
[17] |
H. Matui, Homology and topological full groups of étale groupoids on totally disconnected spaces, Proc. London Math. Soc. (3), 104 (2012), 27-56.
doi: 10.1112/plms/pdr029. |
[18] |
I. F. Putnam, The $C^*$-algebras associated with minimal homeomorphisms of the Cantor set, Pacific J. Math., 136 (1989), 329-353. |
[19] |
M. Rφrdam, Classification of Cuntz-Krieger algebras, K-theory, 9 (1995), 31-58.
doi: 10.1007/BF00965458. |
[20] |
M. Rφrdam, F. Larsen and N. J. Laustsen, "An Introduction to K-Theory for $C^*$-Algebras," London Mathematical Society Student Texts, 49, Cambridge University Press, Cambridge, 2000. |
[21] |
J. Spielberg, Free-product groups, Cuntz-Krieger algebras, and covariant maps, Internat. J. Math., 2 (1991), 457-476.
doi: 10.1142/S0129167X91000260. |
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