  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.
