Abstract

We prove that the mapping class group of a compact surface with a finite number of punctures and non-empty boundary is order automatic. More precisely, the group is right-orderable, has an automatic structure as described by Mosher, and there exists a finite state automaton that decides, given the Mosher normal forms of two elements of the group, which of them represents the larger element of the group. Moreover, the decision takes linear time in the length of the normal forms.

Authors