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Quantum Topology

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Volume 8, Issue 1, 2017, pp. 35–73
DOI: 10.4171/QT/86

Published online: 2017-03-23

Generalized Kashaev invariants for knots in three manifolds

Jun Murakami[1]

(1) Waseda University, Tokyo, Japan

Kashaev’s invariants for a knot in a three sphere are generalized to invariants of a knot in a three manifold. A relation between the newly constructed invariants and the hyperbolic volume of the knot complement is observed for some knots in lens spaces.

Keywords: Knots, three manifolds, hyperbolic manifolds, quantum groups, Hopf algebras

Murakami Jun: Generalized Kashaev invariants for knots in three manifolds. Quantum Topol. 8 (2017), 35-73. doi: 10.4171/QT/86