Gauge Theory and Topology Seminar: Complex Chern-Simons invariants of 3-manifolds via abelianization


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November 10, 2023 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Dan Freed - Harvard

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. The locality of the Chern-Simons invariant, expressed in the language of topological field theory, plays an important role. The dilogarithm arises from a novel construction involving Chern-Simons invariants of flat C*-connections over a 2-torus.