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SUMMARY:Signature and Toledo Invariants for Flat Unitary Bundles over Surf
aces with Boundary
DTSTART:20231204T150000Z
DTEND:20231204T161500Z
DTSTAMP:20240222T001900Z
UID:indico-event-11023@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Inkang Kim (KIAS)\n\nWe consider representations of
the fundamental groups of compact surfaces with boundary into classical si
mple Lie groups of Hermitian type. We relate work on the signature of the
associated local systems\, due to Meyer and Atiyah\, to Burger-Iozzi-Wienh
ard's Toledo invariant. To measure the difference\, we extend Atiyah-Patod
i-Singer's rho invariant\, initially defined on U(p)\, to discontinuous cl
ass 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 Burge
r-Iozzi-Wienhard's version. This is joint work with P. Pansu and X. Wan.\n
\nhttps://indico.math.cnrs.fr/event/11023/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/11023/
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