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Authors
Kevin Whyte
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We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees with Abelian stabilizers, which we are able to classify completely.
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We construct examples of fibered three-manifolds with first Betti number at least 2 and with fibered faces all of whose monodromies extend to a handlebody.
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We generalize Bestvinas notion of a $mathcal{Z}$-boundary for a group to that of a coarse $mathcal{Z}$-boundary. We show that established theorems about $mathcal{Z}$-boundaries carry over nicely to the more general theory, and that some wished-for properties of $mathcal{Z}$-boundaries become theorems when applied to coarse $mathcal{Z}$-boundaries. Most notably, the property of admitting a coarse $mathcal{Z}$-boundary is a pure quasi-isometry invariant. In the process, we streamline both new and existing definitions by introducing the notion of a model $mathcal{Z}$-geometry. In accordance with the existing theory, we also develop an equivariant version of the above -- that of a coarse $Emathcal{Z}$-boundary.
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