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Simple connectivity
of the Markov partition space
L. Badoian and J.B. Wagoner |
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Vol. 193 (2000), No. 1, 1–4
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Abstract |
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In Wagoner, 1987 the simplicial complex PA of Markov partitions was introduced as a tool for studying the group of automorphisms of a subshift of finite type (XA,σA) built from a zero-one transition matrix A. Triangles in PA led to the matrix Triangle Identities in Wagoner, Pac. Journal, 1990 which have been used in Wagoner, 1990, 1990, 1990, 1992, Kim, Roush & Wagoner, 1992, and the Williams Conjecture counterexample paper Kim & Roush, to appear. A key fact about PA is that it is contractible. See Wagoner, 1987. The purpose of this note is to correct the proof on pp. 99-100 in Wagoner, 1987 that PA is simply connected and in the process to improve the bound in Proposition 2.13 of Wagoner, 1987. |
Milestones
Received: 5 May 1998
Published: 1 March 2000
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Authors |
| L. Badoian | |
| Department of Mathematics University of California Berkeley, CA 94720 |
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| J.B. Wagoner | |
| Department of Mathematics University of California Berkeley, CA 94720 |
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