# Genealogy of Non-perturbative Quantum-Invariants of 3-Manifolds: The Surgical Family

@article{Kerler1995GenealogyON,
title={Genealogy of Non-perturbative Quantum-Invariants of 3-Manifolds: The Surgical Family},
author={Thomas Kerler},
journal={arXiv: Quantum Algebra},
year={1995}
}
• T. Kerler
• Published 21 January 1996
• Mathematics, Physics
• arXiv: Quantum Algebra
We study the relations between the invariants $\tau_{RT}$, $\tau_{HKR}$, and $\tau_L$ of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko, respectively. In particular, we discuss explicitly how $\tau_L$ specializes to $\tau_{RT}$ for semisimple categories and to $\tau_{HKR}$ for Tannakian categories. We give arguments for that $\tau_L$ is the most general invariant that stems from an extended TQFT. We introduce a canonical, central element, {\sf Q}, for a quasi-triangular Hopf…
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