Abstract: In this talk we introduce the notion of Toledo invariant for representations of the fundamental group of a higher dimensional Kähler manifold $X$ into a non-compact Lie group of Hermitian type $G$. The usual Milnor-Wood inequality easily generalizes if one makes the further assumption that there exist a holomorphic equivariant map from the universal cover $\tilde X$ of $X$ to the (Kähler) symmetric space of $G$. We classify the maximal ones among these (i.e. the ones satisfying the equality in the above inequality), that turn out to be rigid. In particular, it follows that, to prove the rigidity conjecture for maximal representations of cocompact complex hyperbolic lattices, it is enough to prove that every maximal representation can be deformed to one admitting a holomorphic equivariant map. The proof is based on Higgs bundles techniques; we will overview how the concepts introduced in this talk can be effectively restated in Higgs bundles terms in order to give easy proofs of some statements.
Hinweis: Comment: Um 13:00 Uhr gemeinsamer Imbiss im Seifertraum, EG, INF 288
Dienstag, den 5. Mai 2015 um 13:30 Uhr, in INF288, HS5 Dienstag, den 5. Mai 2015 at 13:30, in INF288, HS5
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Professor Anna Wienhard