Skein-theoretical derivation of some formulas of Habiro
By Gregor Masbaum. 2003
107 citations recorded by the source corpus.
We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl 2 invariants of integral homology 3-spheres. Habiro originally derived these formulas using the quantum group U q sl 2 . As an application, we give a formula for the colored Jones polynomial of twist knots, generalizing formulas of Habiro and Le for the trefoil and the figure eight knot.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/941d1557ed1d3a49cc8de5d92c235483b6367d48
How researchers see this paper
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In Geometry and Topology
- Stavros Garoufalidis
- Hitoshi Murakami
- Yoshiyuki Yokota
- Kazuo Habiro
- Kazuhiro Hikami
- Sergei Gukov
- Tudor Dimofte
- Jun Murakami
In Mathematical Physics
- Stavros Garoufalidis
- Hitoshi Murakami
- Yoshiyuki Yokota
- Kazuo Habiro
- Jun Murakami
- P. Teichner
- Benson Farb
- Tim D. Cochran
Citations in the corpus
- Torus knots and quantum modular forms (2014, unknown): “, [12,20,24]) JN (T(2,3); q) = q1−N ∞ ∑ n=0 q−nN ( q1−N ) n , (1.”
- On the characteristic and deformation varieties of a knot (2003, background): “5 + n 3 3 + n q (-q + q ) SUM[n] Out[ 12 ]= ------------------------------ -”
- A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres (2006, methodology): “The case for Ki,±1, i ∈ Z, (and essentially L±1) has been proved by Masbaum [58] using skein theory.”
- The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces (2004, background): “Le showed that the colored Jones polynomial JNðE; tÞ of the figure-eight knot E is given as follows (see also [6]):”