Generalized kashaev invariants for knots in three manifolds

Jun Murakami

doi:10.4171/QT/86

Generalized kashaev invariants for knots in three manifolds

Jun Murakami^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	35-73
Number of pages	39
Journal	Quantum Topology
Volume	8
Issue number	1
DOIs	https://doi.org/10.4171/QT/86
Publication status	Published - 2017

Keywords

Hopf algebras
Hyperbolic manifolds
Knots
Quantum groups
Three manifolds

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

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10.4171/QT/86

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title = "Generalized kashaev invariants for knots in three manifolds",

abstract = "Kashaev{\textquoteright}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 = "Hopf algebras, Hyperbolic manifolds, Knots, Quantum groups, Three manifolds",

author = "Jun Murakami",

note = "Funding Information: This work was supported in part by JSPS KAKENHI Grant Nr. 22540236, 25287014. Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2017",

doi = "10.4171/QT/86",

language = "English",

volume = "8",

pages = "35--73",

journal = "Quantum Topology",

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publisher = "European Mathematical Society Publishing House",

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AU - Murakami, Jun

N1 - Funding Information: This work was supported in part by JSPS KAKENHI Grant Nr. 22540236, 25287014. Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Hopf algebras

KW - Hyperbolic manifolds

KW - Knots

KW - Quantum groups

KW - Three manifolds

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ER -

Generalized kashaev invariants for knots in three manifolds

Abstract

Keywords

ASJC Scopus subject areas

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