Skeins and handlebodies
In a \((2+1)\)-topological quantum field theory one associates a vector space to a closed surface and a vector to a 3-manifold bounded by the surface. The author expresses a base of the vector space corresponding to the SU(2) theory in terms of the Kauffman linear skein in a handlebody embedded in \(S^ 3\) by using the Temperley-Lieb algebra. The dimension of this vector space is confirmed in [J. Knot Theory Ramifications 2, No. 2, 171-194 (1993; Zbl 0793.57003)] to be equal to the SU(2) quantum invariant of the product of the closed surface and a circle, which is predicted in \textit{M. F. Atiyah} [The geometry and physics of knots (1990; Zbl 0729.57002)].
\((2+1)\)-topological quantum field theory
scientific article; zbMATH DE number 509120
scientific article