The 3D-index and normal surfaces

Stavros Garoufalidis; Craig Hodgson; Neil Hoffman; Hyam Rubinstein

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arXiv · 1604.02688

The 3D-index and normal surfaces

Stavros Garoufalidis·Craig Hodgson·Neil Hoffman·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.

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Stavros Garoufalidis, Craig Hodgson, Neil Hoffman, Hyam Rubinstein. 2016-04-10. The 3D-index and normal surfaces. https://arxiv.org/abs/1604.02688

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