The volume and Chern-Simons invariant of a representation

By C. Zickert. 2007

83 citations recorded by the source corpus.

We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,C)-representation of a tame 3-manifold. If the representation is the geometric representation of a hyperbolic 3-manifold, our formula computes the volume and Chern-Simons invariant directly from an ideal triangulation with no use of additional combinatorial topology. In particular, the Chern-Simons invariant is computed just as easily as the volume.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/62f44edb41f4a2dec74c5fd57b47e4701e8a73fb

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In Computational Theory and Mathematics

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Citations in the corpus

An Introduction to the Volume Conjecture (2010, background): “For combinatorial approaches to the Chern–Simons invariant, see [32] and [44].”
Gluing equations for PGL(n, ℂ)–representations of 3–manifolds (2012, methodology): “8 Decorations We refer to Garoufalidis, Thurston and Zickert [16] or Zickert [25] for more details on decorations.”
The complex volume of SL(n,C)-representations of 3-manifolds (2011, background): “Section 3 gives a brief review of the two variants of the extended Bloch group, and Section 4 reviews the theory, introduced in Zickert [28], of decorated representations and relative fundamental classes.”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “This can be seen explicitly either from constructions involving three-dimensional developing maps [59, 62], or from more combinatorial viewpoints as in [55].”