Illinois Journal of Mathematics

The 3D-index and normal surfaces

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1498032034

Mathematical Reviews number (MathSciNet)
MR3665182

Zentralblatt MATH identifier
1378.57030

Subjects
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}

Citation

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. https://projecteuclid.org/euclid.ijm/1498032034


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