Special Physics/Math Seminar

Complex Chern-Simons invariants of 3-manifolds and abelianization

Dan Freed, Department of Mathematics, University of Texas at Austin,

A hyperbolic 3-manifold M carries a flat PSL(2;C)-connection whose Chern-Simons invariant has been much studied since the early 1980's. For example, its real part is the volume of M. Explicit formulas in terms of a triangulation involve the dilogarithm. In joint work with Andy Neitzke we use 3-dimensional spectral networks to abelianize the computation of complex Chern-Simons invariants. In the process we locate the dilogarithm function in spin abelian Chern-Simons theory.

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