标题： 三维指标与正规曲面 显示英文标题

标题： The 3D-index and normal surfaces

摘要： 迪莫夫特、盖托和古科夫引入了一个强有力的不变量，即与带有环边的三维流形的一个合适理想三角剖分相关的3D指标。 3D指标是一组在 $q^{1/2}$ 中具有整数系数的形式幂级数。 我们的目标是解释3D指标如何成为与该理想三角剖分相关的法向曲面的生成函数。 这表明了3D指标与经典的法向曲面理论之间的联系，并实现了通过法向曲面构造三维流形拓扑不变量的梦想。 显示英文摘要

摘要： Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in $q^{1/2}$ with integer coefficients. Our goal is to explain how the 3D-index is a generating series of normal surfaces associated to the ideal triangulation. This shows a connection of the 3D-index with classical normal surface theory, and fulfills a dream of constructing topological invariants of 3-manifolds using normal surfaces.