Order automatic mapping class groups

Pacific Journal of Mathematics ORDER AUTOMATIC MAPPING CLASS GROUPS

of Mathematics ORDER AUTOMATIC MAPPING CLASS GROUPS

2 Order Automatic Mapping Class

We prove that the mapping class group of a compact surface with a nite 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 nite state automaton that decides, given the Mosher normal forms of two elements of the group, which of them represents the larger element of the g...

Order automatic mapping class

We prove that the mapping class group of a compact surface with a nite 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 nite state automaton that decides, given the Mosher normal forms of two elements of the group, which of them represents the larger element of the g...

Quasi-homomorphisms on Mapping Class Groups

We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasihomomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping class group is not boundedly generated by these subgroups. In this note we enlarge the class of such subgroups. The generalization is motivated by consideratio...