Orderings of mapping class groups after Thurston
Abstract
We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with a hyperbolic structure, embedding the universal cover in the hyperbolic plane, and extending the action of the mapping class group on it to its limit points on the circle at infinity. We classify all orderings of braid groups which arise in this way. Moreover, restricting to a certain class of ``nonpathological'' orderings, we prove that there are only finitely many conjugacy classes of such orderings.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1999
 arXiv:
 arXiv:math/9907104
 Bibcode:
 1999math......7104S
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory;
 20F36 (Primary) 20F60;
 57M07;
 57M60 (Secondary)
 EPrint:
 32 pages, 10 figures