Bounds on Volume Increase under Dehn Drilling Operations

Details Bounds on Volume Increase under Dehn Drilling Operations Bounds on Volume Increase under Dehn Drilling Operations

1995-06-13

arxiv.org/abs/math/9506209v1

Mathematics

Geometric Topology

Scientific paper

In this paper we investigate how the volume of hyperbolic manifolds increases under the process of removing a curve, that is, Dehn drilling. If the curve we remove is a geodesic we are able to show that for a certain family of manifolds the volume increase is bounded above by $\pi \cdot l$ where $l$ is the length of the geodesic drilled. Also we construct examples to show that there is no lower bound to the volume increase in terms of a linear function of a positive power of length and in particular volume increase is not bounded linearly in length.

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