Maximal Decomposition of the Turaev-Viro TQFT

Jerome Petit

doi:https://doi.org/10.14445/22315373/IJMTT-V54P563

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 7 | Year 2018 | Article Id. IJMTT-V54P563 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P563

Maximal Decomposition of the Turaev-Viro TQFT

Jerome Petit

Citation :

Jerome Petit, "Maximal Decomposition of the Turaev-Viro TQFT," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 7, pp. 523-536, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P563

Abstract

In[1]we have built aHQFT from the universal graduation of a spherical category. In the present paper, we show that every graduation (G, p) of a spherical category C defines a Turaev-Viro HQFT. Furthermore we show that the Turaev-Viro TQFT will be split into blocks coming from this HQFT. We show that this decomposition is maximal for the universal graduation of the category, which means that for every graduation (G, p) we define a HQFT which will be split into blocks coming from the HQFT obtained from the universal graduation.

Keywords

Quantum invariants, Turaev-Viro invariant, TQFTs, HQFTs

References

[1] J. Petit, "Decomposition of the Tuarev-Viro TQFT," arxiv math/0903.4512v1, 2009.
[2] V. Turaev and O. Viro, "State sum invariants of 3-manifolds and quantum 6j-symbol," Topology, vol. 31, pp. 865-902, 1992.
[3] J. Barrett and B. Westbury, "Invaraints of piecewise-linear 3-manifolds," Trans. Amer. Math. Soc., vol. 10, no. 348, pp. 3997- 4022, 1996.
[4] I. Gelfand and D. Kazhdan, "Invariant of three dimensional manifolds," Geometric and Functionnal Analysis, no. 6, pp. 268-300, 1996.
[5] V. Turaev, Quantum invariants of knots and 3-manifolds, Walter de Gruyter, 1994.
[6] V. Turaev, "Homotopy field theory in dimension 3 and crossed group-categories," arxiv math/0005291, 2000.