半充分闭合编织物和体积
Semi-Adequate Closed Braids and Volume
摘要：
在本文中，我们证明了一个家庭的A-适当的封闭辫子的体积可以有界上下的扭曲数，辫子串的数量，可以从一个给定的封闭辫子图的组合学读取的数量。我们还表明，许多这些封闭的辫子的体积可以有界的一个单一的稳定系数的有色琼斯多项式，从而表明，这个集合的封闭辫子满足粗体积猜想。通过扩展到一个更广泛的家庭封闭的辫子，我们也得到了体积界的数量方面的积极和消极的扭曲区域在一个给定的封闭的辫子图。此外，对于一个家庭的A-适当的封闭3-辫子，我们表明，体积可以有界的参数$s$从Schreier正常形式的3-辫子。最后，我们表明，对于同一个家庭的A-适当的封闭3-辫子，参数$k$和$s$从Schreier规范形式实际上可以读出原来的3-辫子字。
英文摘要：
In this paper, we show that the volumes for a family of A-adequate closed braids can be bounded above and below in terms of the twist number, the number of braid strings, and a quantity that can be read from the combinatorics of a given closed braid diagram. We also show that the volumes for many of these closed braids can be bounded in terms of a single stable coefficient of the colored Jones polynomial, thus showing that this collection of closed braids satisfies a Coarse Volume Conjecture. By expanding to a wider family of closed braids, we also obtain volume bounds in terms of the number of positive and negative twist regions in a given closed braid diagram. Furthermore, for a family of A-adequate closed 3-braids, we show that the volumes can be bounded in terms of the parameter $s$ from the Schreier normal form of the 3-braid. Finally we show that, for the same family of A-adequate closed 3-braids, the parameters $k$ and $s$ from the Schreier normal form can actually be read off of the original 3-braid word.
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