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Turaev torsion invariants of 3-orbifolds

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Abstract

We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an understanding of how the components of the invariant change when we remove a curve from the singular set. The second is a formula relating the invariant of the 3-orbifold to the Turaev torsion invariant of the underlying 3-manifold in the case when the singular set is a nullhomologous knot.

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Acknowledgments

The author would like to thank Weimin Chen for suggesting this problem and for helpful conversations. The author is grateful to Danny Ruberman for his support and advice and for carefully reading an early draft of the paper. The author would also like to thank the reviewer for helpful comments. A part of this work was supported by an NSF IGERT fellowship under grant number DGE-1068620 and the NSF FRG grant DMS-1065784.

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Authors and Affiliations

  1. Department of Mathematics, Brandeis University, MS 050, 415 South Street, Waltham, MA, 02453, USA

    Biji Wong

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  1. Biji Wong
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Correspondence to Biji Wong.

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Wong, B. Turaev torsion invariants of 3-orbifolds. Geom Dedicata 187, 179–197 (2017). https://doi.org/10.1007/s10711-016-0196-7

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  • DOI: https://doi.org/10.1007/s10711-016-0196-7

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