Reflection equation and link polynomials for arbitrary genus solid tori

Details Reflection equation and link polynomials for arbitrary genus solid tori Reflection equation and link polynomials for arbitrary genus solid tori

1993-01-08

arxiv.org/abs/hep-th/9301023v2

Physics

High Energy Physics

High Energy Physics - Theory

17 pages + 8 postscript figures

Scientific paper

The correspondence between the braid group on a solid torus of arbitrary genus and the algebra of Yang-Baxter and reflection equation operators is shown. A representation of this braid group in terms of $R$-matrices is given. The characteristic equation of the reflection equation matrix is considered as an additional skein relation. This could lead to an intrinsic definition of invariant link polynomials on solid tori and, via Heegaard splitting, to invariant link polynomials on arbitrary three-manifolds without boundary.

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