Simple connectivity of the Markov partition space

In Wagoner, 1987 the simplicial complex P-A of Markov partitions was introd uced as a tool for studying the group of automorphisms of a subshift of fin ite type (X-A, sigma(A)) built from a zero-one transition matrix A. Triangl es in P-A led to the matrix Triangle Identities in Wagoner, Pac. Journal, 1 990 which have been used in Wagoner, 1990, 1990, 1990, 1992, Kim, Roush & W agoner, 1992, and the Williams Conjecture counterexample paper Kim & Roush, to appear. A key fact about P-A is that it is contractible. See Wagoner, 1987. The pur pose of this note is to correct the proof on pp. 99-100 in Wagoner, 1987 th at P-A is simply connected and in the process to improve the bound in Propo sition 2.13 of Wagoner, 1987.