Decomposition of the Turaev-Viro TQFT

Details Decomposition of the Turaev-Viro TQFT Decomposition of the Turaev-Viro TQFT

2009-03-26

arxiv.org/abs/0903.4512v1

Mathematics

Quantum Algebra

Scientific paper

We show that for every spherical category $\C$ with invertible dimension, the Turaev-Viro TQFT admits a splitting into blocks which come from an HQFT, called the Turaev-Viro HQFT. The Turaev-Viro HQFT has the classifying space $B\grad$ as target space, where $\grad$ is a group obtained from the category $\C$. This construction gives a reformulation of the Turaev-Viro TQFT in terms of HQFT. Furthermore the Turaev-Viro HQFT is an extension of the \emph{homotopical Turaev-Viro invariant} which splits the Turaev-Viro invariant. An application of this result is a description of the homological twisted version of the Turaev-Viro invariant in terms of HQFT.

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