Illinois Journal of Mathematics

The 3D-index and normal surfaces

Stavros Garoufalidis, Craig D. Hodgson, Neil R. Hoffman, and J. Hyam Rubinstein

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}


Garoufalidis, Stavros; Hodgson, Craig D.; Hoffman, Neil R.; Rubinstein, J. Hyam. The 3D-index and normal surfaces. Illinois J. Math. 60 (2016), no. 1, 289--352. doi:10.1215/ijm/1498032034.

Export citation