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- Helge Glöckner, Ralf Gramlich, Tobias Hartnick
- 2008

We study final group topologies and their relations to compactness properties. In particular, we are interested in situations where a colimit or direct limit is locally compact, a k ω-space, or locally k ω. As a first application, we show that unitary forms of complex Kac-Moody groups can be described as the colimit of an amalgam of subgroups (in the… (More)

- TOBIAS HARTNICK
- 2009

We 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 degree primitive elements. Our proof uses a Hirzebruch type… (More)

- TOBIAS HARTNICK
- 2008

We show by elementary combinatorial arguments that any non-zero homogeneous quasimorphism on a given group can be realized as the relative growth of some bi-invariant partial order on that group. Thereby we provide a link between quasimorphisms, bounded cohomol-ogy and partial orders. This yields existence results for bi-invariant partial orders, e.g. for… (More)

- TOBIAS HARTNICK
- 2009

We 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. Any maximal… (More)

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