Triangle identities and symmetries of a subshift of finite type

Abstract

We prove the group Aut(^) of symmetries of a subshift of finite type is isomorphic to the fundamental group of the space RS(^) of strong shift equivalences built from the algebraic RS Triangle Identities for zero-one matrices which arise from triangles in the contractable simplicial complex of Markov partitions. Moreover, we show the higher homotopy groups of RS(< ^) are zero. RS(< ^) is therefore homotopy equivalent to the classifying space of Aut(^).