Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 6 (2017), 3341-3373.
The localized skein algebra is Frobenius
When in the Kauffman bracket skein relation is set equal to a primitive root of unity with not divisible by , the Kauffman bracket skein algebra of a finite-type surface is a ring extension of the –character ring of the fundamental group of . We localize by inverting the nonzero characters to get an algebra over the function field of the corresponding character variety. We prove that if is noncompact, the algebra is a symmetric Frobenius algebra. Along the way we prove is finitely generated, is a finite-rank module over the coordinate ring of the corresponding character variety, and learn to compute the trace that makes the algebra Frobenius.
Algebr. Geom. Topol., Volume 17, Number 6 (2017), 3341-3373.
Received: 11 January 2015
Revised: 11 May 2017
Accepted: 27 May 2017
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds
Abdiel, Nel; Frohman, Charles. The localized skein algebra is Frobenius. Algebr. Geom. Topol. 17 (2017), no. 6, 3341--3373. doi:10.2140/agt.2017.17.3341. https://projecteuclid.org/euclid.agt/1510841508