In Wagoner, 1987 the simplicial complex $P_A$ of Markov partitions was introduced as a tool for studying the group of automorphisms of a subshift of finite type $(X_A, \sigma_A)$ built from a zero-one transition matrix $A$. Triangles in $P_A$ 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 $P_A$ 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 $P_A$ is simply connected and in the process to improve the bound in Proposition 2.13 of Wagoner, 1987.