On the Kauffman bracket skein module of the quaternionic manifold

Abstract

We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A,A^{-1}] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z_2 homology of the manifold, we determine that they are linearly independent.

corrected summation signs in figures 14, 15, 17. Other minor changes

References in corpus (1)

• The Kauffman bracket skein module of a twist knot exterior

Cited by in corpus (3)

• Infinite families of hyperbolic $3$-manifolds with finite dimensional skein modules
• Kauffman bracket skein modules of small 3-manifolds
• A basis for the Kauffman skein module of the product of a surface and a circle