Séminaire Géométrie et groupes discrets

Signature and Toledo Invariants for Flat Unitary Bundles over Surfaces with Boundary

by Inkang Kim (KIAS)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

We consider representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems, due to Meyer and Atiyah, to Burger-Iozzi-Wienhard's Toledo invariant. To measure the difference, we extend Atiyah-Patodi-Singer's rho invariant, initially defined on U(p), to discontinuous class functions, first on U(p,q), and then on other classical groups via embeddings into U(p,q). As an application, we obtain a Milnor-Wood type inequality which slightly differs from, and sometimes improves upon Burger-Iozzi-Wienhard's version. This is joint work with P. Pansu and X. Wan.

Organized by

Fanny Kassel