Tobias Hartnick
Reconstructing quasimorphisms from associated partial orders and a question of Polterovich.
Wed, 12/02/2009 - 16:01 — SomNambulAuthors: Tobias Hartnick, Gabi Ben Simon
Subjects: Group Theory
AbstractWe show that every continuous homogeneous quasimorphism on a
finite-dimensional 1-connected simple Lie group arises as the relative growth
of some continuous bi-invariant partial order on that group.Surjectivity of the comparison map in bounded cohomology for Hermitian Lie groups.
Wed, 12/02/2009 - 16:01 — SomNambulAuthors: Tobias Hartnick, Andreas Ott
Subjects: Algebraic Topology
AbstractWe prove surjectivity of the comparison map from continuous bounded
cohomology to continuous cohomology for Hermitian Lie groups with finite
center. For general semisimple Lie groups with finite center, the same argument
shows that the image of the comparison map contains all the even generators.
Our proof uses a Hirzebruch type proportionality principle in combination with
Gromov's results on boundedness of primary characteristic classes and classical
results of Cartan and Borel on the cohomology of compact homogeneous spaces.Cross ratios associated with maximal representations.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Tobias Hartnick, Tobias Strubel
Subjects: Differential Geometry
AbstractWe define a generalization of the classical four-point cross ratio of
hyperbolic geometry on the unit circle given by invariant functions on Shilov
boundaries of arbitrary bounded symmetric domains of tube type. This
generalization is functorial and well-behaved under products. In fact, these
two properties determine our extension uniquely.
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