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Quantum invariants at the sixth root of unity

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Abstract

A general topological formula is given for theSU (2) quantum invariant of a 3-manifoldM at the sixth root of unity. It is expressed in terms of the homology, Witt invariants and signature defects of the various 2-fold covers ofM, and thus ties in with basic 4-dimensional invariants. A discussion of the range of values of these quantum invariants is included, and explicit evaluations are made for lens spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Robion Kirby

  2. Department of Mathematics, Bryn Mawr College, 19010, Bryn Mawr, PA, USA

    Paul Melvin

  3. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, BC, Canada

    Xingru Zhang

Authors
  1. Robion Kirby
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  2. Paul Melvin
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  3. Xingru Zhang
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Communicated by N.Yu. Reshetikhin

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Kirby, R., Melvin, P. & Zhang, X. Quantum invariants at the sixth root of unity. Commun.Math. Phys. 151, 607–617 (1993). https://doi.org/10.1007/BF02097030

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  • DOI: https://doi.org/10.1007/BF02097030

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