The Toledo invariant on smooth varieties of general type

Details The Toledo invariant on smooth varieties of general type The Toledo invariant on smooth varieties of general type

2008-10-27

arxiv.org/abs/0810.4805v1

Mathematics

Differential Geometry

19 pages

Scientific paper

We propose a definition of the Toledo invariant for representations of fundamental groups of smooth varieties of general type into semisimple Lie groups of Hermitian type. This definition allows to generalize the results known in the classical case of representations of complex hyperbolic lattices to this new setting: assuming that the rank of the target Lie group is not greater than two, we prove that the Toledo invariant satisfies a Milnor-Wood type inequality and we characterize the corresponding maximal representations.

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