## Illinois Journal of Mathematics

### The 3D-index and normal surfaces

#### Abstract

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.

#### Article information

Source
Illinois J. Math., Volume 60, Number 1 (2016), 289-352.

Dates
Revised: 17 December 2016
First available in Project Euclid: 21 June 2017