论文标题
在瑟斯顿规范的双单位球上
On dual unit balls of Thurston norms
论文作者
论文摘要
Thurston规范是在其第二个同源矢量空间上定义的3个manifolds的不变性，并且了解双单位球的形状是一个（广泛的）开放问题。 W. Thurston表明，Z^2中的每个对称多边形（其顶点都满足奇偶校验特性）是瑟斯顿标准的双单位球上的3个序列。但是，尚不清楚多面体顶点上的奇偶校验特性在更高维度上是足够的条件，还是它们是多型的，具有mod 2一致性的顶点，无法实现为瑟斯顿规范的双单位球。在本文中，我们在Z^2G中提供了一系列的多型家族，可以将其视为3个manifolds上瑟斯顿规范的双单位球。这些多面体来自定向封闭表面上的交点规范，本文扩大了这两个规范之间的桥梁。
Thurston norms are invariants of 3-manifolds defined on their second homology vector spaces, and understanding the shape of their dual unit ball is a (widely) open problem. W. Thurston showed that every symmetric polygon in Z^2, whose vertices satisfy a parity property, is the dual unit ball of a Thurston norm on a 3-manifold. However, it is not known if the parity property on the vertices of polytopes is a sufficient condition in higher dimension or if their are polytopes, with mod 2 congruent vertices, that cannot be realized as dual unit balls of Thurston norms. In this article, we provide a family of polytopes in Z^2g that can be realized as dual unit balls of Thurston norms on 3-manifolds. These polytopes come from intersection norms on oriented closed surfaces and this article widens the bridge between these two norms.
