Non-semisimple 3-manifold invariants derived from the Kauffman bracket

Marco De Renzi; Jun Murakami

doi:10.4171/QT/164

Non-semisimple 3-manifold invariants derived from the Kauffman bracket

Marco De Renzi, Jun Murakami

School of Fundamental Science and Engineering

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

1 Citation (Scopus)

Abstract

We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of sl₂ using purely combinatorial meth-ods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten–Reshetikhin–Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.

Original language	English
Pages (from-to)	255-333
Number of pages	79
Journal	Quantum Topology
Volume	13
Issue number	2
DOIs	https://doi.org/10.4171/QT/164
Publication status	Published - 2022

Keywords

Kauffman bracket
Quantum invariants
Temperley–Lieb algebras
quantum groups

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

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10.4171/QT/164

Cite this

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title = "Non-semisimple 3-manifold invariants derived from the Kauffman bracket",

abstract = "We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of sl2 using purely combinatorial meth-ods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten–Reshetikhin–Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.",

keywords = "Kauffman bracket, Quantum invariants, Temperley–Lieb algebras, quantum groups",

author = "{De Renzi}, Marco and Jun Murakami",

note = "Funding Information: Funding. This work was supported by KAKENHI Grant-in-Aid for JSPS Fellows 19F19765. Publisher Copyright: {\textcopyright} 2022, European Mathematical Society Publishing House. All rights reserved.",

year = "2022",

doi = "10.4171/QT/164",

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journal = "Quantum Topology",

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T1 - Non-semisimple 3-manifold invariants derived from the Kauffman bracket

AU - De Renzi, Marco

AU - Murakami, Jun

N1 - Funding Information: Funding. This work was supported by KAKENHI Grant-in-Aid for JSPS Fellows 19F19765. Publisher Copyright: © 2022, European Mathematical Society Publishing House. All rights reserved.

PY - 2022

Y1 - 2022

N2 - We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of sl2 using purely combinatorial meth-ods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten–Reshetikhin–Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.

AB - We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of sl2 using purely combinatorial meth-ods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten–Reshetikhin–Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.

KW - Kauffman bracket

KW - Quantum invariants

KW - Temperley–Lieb algebras

KW - quantum groups

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JO - Quantum Topology

JF - Quantum Topology

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ER -

Non-semisimple 3-manifold invariants derived from the Kauffman bracket

Abstract

Keywords

ASJC Scopus subject areas

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