Braids, orderings, and minimal volume cusped hyperbolic 3-manifolds

作者：Kin Eiko^*; Rolfsen Dale

来源：Groups, Geometry, and Dynamics, 2018, 12(3): 961-1004.

DOI：10.4171/GGD/460

• Ordered groups
• bi-orderings
• knots and links
• braid groups
• free groups
• mapping class groups
• fibered 3-manifolds

It is well known that there is a faithful representation of braid groups on automorphism groups of free groups, and it is also well known that free groups are biorderable. We investigate which n-strand braids give rise to automorphisms which preserve some bi-ordering of the free group F-n of rank n. As a consequence of our work we find that of the two minimal volume hyperbolic 2-cusped orientable 3-manifolds, one has biorderable fundamental group whereas the other does not. We prove a similar result for the 1-cusped case, and have further results for more cusps. In addition, we study pseudo-Anosov braids and find that typically those with minimal dilatation are not order-preserving.

• 出版日期2018