Braids, orderings and minimal volume cusped hyperbolic 3-manifolds

Eiko Kin; Dale Rolfsen

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arXiv · 1610.03241

Braids, orderings and minimal volume cusped hyperbolic 3-manifolds

Eiko Kin·Dale Rolfsen

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Abstract

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 bi-orderable. We investigate which n-strand braids give rise to automorphisms which preserve some bi-ordering of the free group rank n. As a consequence of our work we find that of the two minimal volume hyperbolic 2-cusped orientable 3-manifolds, one has bi-orderable 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.

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BibTeX RIS

Eiko Kin, Dale Rolfsen. 2016-10-11. Braids, orderings and minimal volume cusped hyperbolic 3-manifolds. https://arxiv.org/abs/1610.03241

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