Geometric and Functional Analysis

, Volume 22, Issue 6, pp 1636–1707 | Cite as

A Combination Theorem for Metric Bundles

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Abstract

We introduce the notion of metric (graph) bundles which provide a coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina–Feighn in the special case that the inclusions of the edge spaces into the vertex spaces are uniform coarsely surjective quasi-isometries. We prove the existence of quasi-isometric sections in this generality. Then we prove a combination theorem for metric (graph) bundles that establishes sufficient conditions, particularly flaring, under which the metric bundles are hyperbolic. We use this to give examples of surface bundles over hyperbolic disks, whose universal cover is Gromov-hyperbolic. We also show that in typical situations, flaring is also a necessary condition.

Keywords

Cayley Graph Short Exact Sequence Mapping Class Group Hyperbolic Group Point Projection 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsRKM Vivekananda University, Belur MathHowrahIndia

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