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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)
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)
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