English

Turaev-Viro invariants as an extended TQFT III

Quantum Algebra 2011-08-31 v2

Abstract

In the third paper in this series, we examine the Reshetikhin-Turaev and Turaev-Viro TQFTs at the level of surfaces. In particular, we show that for a closed surface Σ\Sigma, ZTV,C(Σ)ZRT,Z(\C)(Σ)Z_{TV, \mathcal{C}}(\Sigma) \cong Z_{RT, Z(\C)}(\Sigma), thus extending the equality of 3-manifold invariants proved in an earlier paper to an equivalence of TQFTs. We also describe how to compute Turaev-Viro state sums for 3-manifolds with embedded ribbon graphs.

Keywords

Cite

@article{arxiv.1012.0560,
  title  = {Turaev-Viro invariants as an extended TQFT III},
  author = {Benjamin Balsam},
  journal= {arXiv preprint arXiv:1012.0560},
  year   = {2011}
}

Comments

19 pages, many figures. Added explanation of equivalence of theories for extended 3-manifolds and added description of TV theory for manifolds with embedded ribbon graphs