The infinite associahedron and R. J. Thompson’s group $$T$$ T

Abstract

In this paper we construct a cellular complex which is an infinite analogue to Stasheff's associahedra. We prove that it is contractible and state that its (combinatorial) automorphism group is isomorphic to a semi-direct product of R.J. Thompson's group T with Z/2Z. MSC classification: 20F65, 20F38, 57Q05, 57M07.