Extended Bloch group and the Cheeger-Chern-Simons class

By Walter D. Neumann. 2003

106 citations recorded by the source corpus.

We dene an extended Bloch group and show it is naturally isomorphic to H3(PSL(2;C);Z). Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger{Chern{Simons class on this homology group. It also leads to an independent proof of the analytic relationship between volume and Chern{Simons invariant of hyperbolic 3{manifolds conjectured in [16] and proved in [24], as well as eective formulae for the Chern{Simons invariant of a hyperbolic 3{manifold. AMS Classication numbers Primary: 57M27 Secondary: 19E99, 57T99

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/750f9a1cc8f7e900d9ecc78c12af9ff2b508576b

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Citations in the corpus

The dilogarithm function. (2007, background): “For further discussion of this, see Neumann [33] as well as [32] and [42].”
The complex volume of SL(n,C)-representations of 3-manifolds (2011, methodology): “The formula generalizes the formula in Goette-Zickert [14] for n = 2.”
Chern-Simons theory, analytic continuation and arithmetic (2007, background): “Let us recall those briefly, and refer the reader to [GZ, Wi, Ne , Ga4] for a more detailed discussion.”
Exact results for perturbative Chern-Simons theory with complex gauge group. (2009, methodology): “(21)This expression differs slightly from the one given in [40], because we use 2v + 2πi rather than 2v as the logarithm of the “longitudinal” holonomy, as mentioned in Footnote 13 of Section 3.”