A Combination Theorem for Metric Bundles

By Mahan Mj, Pranab Sardar. 2009

63 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a4d747056a57793e7bd5eb3e64afce9b1aa7ece7

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In Applied Mathematics

1. Spencer Dowdall
2. Samuel J. Taylor

In Geometry and Topology

1. Spencer Dowdall
2. Samuel J. Taylor
3. Jason A. Behrstock
4. Carolyn R. Abbott

Citations in the corpus

• The co‐surface graph and the geometry of hyperbolic free group extensions (2016, background): “8]), p : E → B is an example of the metric graph bundle construction developed by Mj and Sardar in [40].”