Skein spaces and spin structures

Details Skein spaces and spin structures Skein spaces and spin structures

1995-12-22

arxiv.org/abs/gr-qc/9512041v2

Math.Proc.Cambridge Phil.Soc. 126 (1999) 267-275

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, amstex, 15 figures. Revised by a substantial addition to give a geometrical description of all the commutative skein

Scientific paper

10.1017/S0305004198003168

This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an application to Penrose's binor calculus, which is related to the tensor calculus of representations of SU(2). The perspective developed here is that this tensor calculus is actually a calculus of spinors on the plane, and the matrices a re determined by a type of spinor transport which generalises to links in any 3-manifold. A second application shows that there is a skein space which is the algebra of functions on the set of spin structures for the 3-manifold.

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