Observables in the Turaev-Viro and Crane-Yetter models

Barrett, John W.; Garcia-Islas, J. Manuel; Martins, Joao Faria

Observables in the Turaev-Viro and Crane-Yetter models

Authors

Barrett, John W.

Garcia-Islas, J. Manuel

Martins, Joao Faria

Description

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.
Approx 26 pages. v2: 4d results substantially extended