A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres

By Kazuo Habiro. 2006

106 citations recorded by the source corpus.

We construct an invariant JM of integral homology spheres M with values in a completion $\widehat{\mathbb{Z}[q]}$ of the polynomial ring ℤ[q] such that the evaluation at each root of unity ζ gives the the SU(2) Witten–Reshetikhin–Turaev invariant τζ(M) of M at ζ. Thus JM unifies all the SU(2) Witten–Reshetikhin–Turaev invariants of M. It also follows that τζ(M) as a function on ζ behaves like an “analytic function” defined on the set of roots of unity.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66fa340232547f3f8bd0c7647991f8e4457873aa

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In Discrete Mathematics and Combinatorics

1. Jeremy Lovejoy
2. Kazuhiro Hikami
3. Robert Osburn
4. Kathrin Bringmann
5. Frank G. Garvan
6. Chris Jennings-Shaffer

In Geometry and Topology

1. Jeremy Lovejoy
2. Kazuhiro Hikami
3. Robert Osburn
4. Tudor Dimofte
5. Kathrin Bringmann
6. Sergei Gukov

In Mathematical Physics

1. Jeremy Lovejoy
2. Kazuhiro Hikami
3. Tudor Dimofte

Citations in the corpus

• Torus knots and quantum modular forms (2014, background): “Next, recall the cyclotomic expansion of the colored Jones polynomial due to Habiro [13] JN (K ; q) = ∞ ∑ n=0 Cn(K ; q) ( q1+N ) n ( q1−N ) n , (2.”
• Asymptotics of the colored Jones function of a knot (2005, unknown): “Then (see (38)) xj D xn j D xnCj ; (46) zk D n=zn 1 k for 1 k n 1: (47) Using Habiro’s formula for z JL of the Borromean ring [14; 15], one has”