论文标题
胆量，体积和绞线模块的3个模块
Guts, volume and Skein Modules of 3-manifolds
论文作者
论文摘要
我们考虑双曲线链接，这些链接可以接收紧凑，不可还原的3个manifolds的表面上的交替预测。我们表明，在一些温和的假设下，这种链接的补充体积下面是根据表面链路图上定义的kauffman支架函数而言。 如果3个序列是增厚的表面，则该kauffman括号函数会导致琼斯型多项式，这是链接的同位素不变的。我们表明，该多项式的系数在增厚表面的双曲线交替链路的体积上提供了2面线性边界。作为该结果证明的必然性，我们推断出，链接的扭曲数量与磁盘区域交替链接投影，是该链接的不变性。
We consider hyperbolic links that admit alternating projections on surfaces in compact, irreducible 3-manifolds. We show that, under some mild hypotheses, the volume of the complement of such a link is bounded below in terms of a Kauffman bracket function defined on link diagrams on the surface. In the case that the 3-manifold is a thickened surface, this Kauffman bracket function leads to a Jones-type polynomial that is an isotopy invariant of links. We show that coefficients of this polynomial provide 2-sided linear bounds on the volume of hyperbolic alternating links in the thickened surface. As a corollary of the proof of this result, we deduce that the twist number of a reduced, twist reduced, checkerboard alternating link projection with disk regions, is an invariant of the link.
