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Ptolemy coordinates, Dehn invariant and the A-polynomial

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Abstract

We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the \({{\mathrm{SL}}}(2,{\mathbb {C}})\;A\)-polynomial, and more generally the \({{\mathrm{SL}}}(n,{\mathbb {C}})\;A\)-varieties. We also give a formula for the Dehn invariant of an \({{\mathrm{SL}}}(n,{\mathbb {C}})\)-representation.

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Acknowledgments

The author wishes to thank Stavros Garoufalidis, Matthias Goerner and Dylan Thurston for useful conversations, and Fabrice Rouillier for assistance with some of the computations. He also wishes to thank E. Falbel, A. Guilloux, P. V. Koseleff, and F. Rouillier for an invitation to Paris (funded by ANR), leading to many interesting converstations, and to the launch of the project CURVE [8].

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  1. Department of Mathematics, University of Maryland, College Park, MD, 20742-4015, USA

    Christian K. Zickert

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  1. Christian K. Zickert
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Correspondence to Christian K. Zickert.

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The author was supported in part by the NSF Grant DMS-1309088.

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Zickert, C.K. Ptolemy coordinates, Dehn invariant and the A-polynomial. Math. Z. 283, 515–537 (2016). https://doi.org/10.1007/s00209-015-1608-3

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  • DOI: https://doi.org/10.1007/s00209-015-1608-3

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