Skeins and handlebodies
type: Item
instance of: scholarly article
title: Skeins and handlebodies
zbMATH Open document ID: 0805.57010
published in: Pacific Journal of Mathematics
publication date: 1994-03-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 81T99
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 509120
zbMATH Keywords: \((2+1)\)-topological quantum field theory
zbMATH Keywords: Kauffman linear skein in a handlebody
zbMATH Keywords: Temperley-Lieb algebra
zbMATH Keywords: SU(2) quantum invariant
reviewed by: Hitoshi Murakami
MaRDI profile type: Publication
full work available at URL: pjm.1993.159.337
OpenAlex ID: W2141507645
DOI: 10.2140/PJM.1993.159.337
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description: scientific article; zbMATH DE number 509120