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.",

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

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AU - Murakami, Jun

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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

UR - https://www.scopus.com/pages/publications/85128994324

UR - https://www.scopus.com/pages/publications/85128994324#tab=citedBy

U2 - 10.4171/QT/164

DO - 10.4171/QT/164

M3 - Article

AN - SCOPUS:85128994324

SN - 1663-487X

VL - 13

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EP - 333

JO - Quantum Topology

JF - Quantum Topology

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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