Skein spaces and spin structures
摘要
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.
引用
@article{arxiv.gr-qc/9512041,
title = {Skein spaces and spin structures},
author = {John W. Barrett},
journal= {arXiv preprint arXiv:gr-qc/9512041},
year = {2009}
}
备注
9 pages, amstex, 15 figures. Revised by a substantial addition to give a geometrical description of all the commutative skein algebras, for A^6=1 (q^3=1)