Observables in the Turaev-Viro and Crane-Yetter models
Abstract
We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In the case of the three-dimensional invariant, we prove a duality formula relating its Fourier transform to another invariant defined via the coloured Jones polynomial. In the case of the four-dimensional partition function, we give a formula for it in terms of a regular neighbourhood of the 2-complex and the signature of its complement. Some examples are computed which show that the partition function determines an invariant which can detect non locally-flat surfaces in a four-manifold.
Keywords
Cite
@article{arxiv.math/0411281,
title = {Observables in the Turaev-Viro and Crane-Yetter models},
author = {John W. Barrett and J. Manuel Garcia-Islas and Joao Faria Martins},
journal= {arXiv preprint arXiv:math/0411281},
year = {2008}
}
Comments
Approx 26 pages. v2: 4d results substantially extended