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• W3101796646 abstract "For a compact 3-manifold M with arbitrary (possibly empty) boundary, we give a parametrization of the set of conjugacy classes of boundary-unipotent representations of the fundamental group of M into SL(n,C). Our parametrization uses Ptolemy coordinates, which are inspired by coordinates on higher Teichmueller spaces due to Fock and Goncharov. We show that a boundary-unipotent representation determines an element in Neumann's extended Bloch group, and use this to obtain an efficient formula for the Cheeger-Chern-Simons invariant, and in particular for the volume. Computations for the census manifolds show that boundary-unipotent representations are abundant, and numerical comparisons with census volumes, suggest that the volume of a representation is an integral linear combination of volumes of hyperbolic 3-manifolds. This is in agreement with a conjecture of Walter Neumann, stating that the Bloch group is generated by hyperbolic manifolds." @default.
• W3101796646 created "2020-11-23" @default.
• W3101796646 creator A5001204330 @default.
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• W3101796646 date "2015-08-15" @default.
• W3101796646 modified "2023-10-02" @default.
• W3101796646 title "The complex volume of SL(n,C)-representations of 3-manifolds" @default.
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• W3101796646 doi "https://doi.org/10.1215/00127094-3121185" @default.
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