Braids, orderings, and minimal volume cusped hyperbolic 3-manifolds
Braids, orderings, and minimal volume cusped hyperbolic 3-manifolds
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辫状、排序和最小体积尖头双曲 3 流形
DOI：
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发表时间：
2016
期刊：
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通讯作者：
D. Rolfsen
中科院分区：
文献类型：
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作者：
E. Kin;D. Rolfsen
众所周知，自由群的自同构群上存在辫子群的忠实表示，自由群是双序的。我们研究了哪些n-链辫子产生了保持自由群秩n的某些双序的自同构。作为我们工作的结果，我们发现在两个最小体积的双曲2-尖点可定向3-流形中，一个有双序基本群，而另一个没有。对于1-尖点的情形，我们证明了类似的结果，对于更多的尖点，我们得到了进一步的结果。此外，我们还研究了伪Anosov辫子，发现那些具有最小伸缩的辫子通常不保序。
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.