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Cited by 245Geometric and Algebraic TopologyHomotopy and Cohomology in Algebraic TopologyAlgebraic structures and combinatorial models

The DOI matches its Crossref record.

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)

Kauffman, Louis H., Lins, Sostenes·1994·Princeton University Press eBooks
DOI 10.1515/9781400882533
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Abstract

This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

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Metadata

Authors
Kauffman, L. H., & Lins, S.
ORCID
Kauffman, Louis H.
Venue
Princeton University Press eBooks
Publisher
Princeton University Press
Published
1994-12-31
DOI
10.1515/9781400882533
OpenAlex
W4239309077
Cited by
245
References
0
Citations by year
2026: 5 · 2025: 18 · 2024: 10 · 2023: 15 · 2022: 6 · 2021: 4 · 2020: 7 · 2019: 2 · 2018: 7 · 2017: 12 · 2016: 11 · 2015: 10 · 2014: 9 · 2013: 10 · 2012: 6
FWCI
1.21
Type
book
Language
en
Open access
closed
Locations
  • Princeton University Press eBooks (publishedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
  • Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
  • Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
Keywords
Temperley-Lieb algebra, 3-manifold invariants, Jones polynomial, Reshetikhin-Turaev invariants, Turaev-Viro invariants, Kauffman bracket, 4-manifold invariants

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