Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 3 (2011), 1821-1860.
Polynomial $6j$–symbols and states sums
For a given –th root of unity , we give explicit formulas of a family of –variable Laurent polynomials with coefficients in that encode the –symbols associated with nilpotent representations of . For a given abelian group , we use them to produce a state sum invariant of a quadruplet (compact –manifold , link inside , homology class , homology class ) with values in a ring related to . The formulas are established by a “skein” calculus as an application of the theory of modified dimensions introduced by the authors and Turaev in [Compos. Math. 145 (2009) 196–212]. For an oriented –manifold , the invariants are related to defined by the authors and Turaev in [arXiv:0910.1624] from the category of nilpotent representations of . They refine them as where correspond to with the isomorphism .
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1821-1860.
Received: 13 July 2010
Accepted: 8 October 2010
First available in Project Euclid: 19 December 2017
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Geer, Nathan; Patureau-Mirand, Bertrand. Polynomial $6j$–symbols and states sums. Algebr. Geom. Topol. 11 (2011), no. 3, 1821--1860. doi:10.2140/agt.2011.11.1821. https://projecteuclid.org/euclid.agt/1513715247