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Topology/Geometry Seminar

Toledo invariant and surface group representations in SP(2n,R)

Inkang Kim (KIAS)

Location:  zoom link:
Date & time: Tuesday, 09 March 2021 at 3:50PM - 4:50PM

Recently a great deal of attention has been given to the space of surface group representations utilizing various geometric structures, and invariants. In this talk, we present a new approach to this problem, using Atiyah-Patodi-Singer index theory for the surface with boundary. We will calculate the signature formula in this context, and relate it to the Toledo invariant when the target group is a real symplectic group Sp(2n,R). We also present a version of Milnor-Wood type inequality in this context. This is a joint work with Pierre Pansu and Xueyuan Wan.

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