Collars in Complex and Quaternionic Hyperbolic Manifolds |
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Authors: | Sarah Markham John R Parker |
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Institution: | (1) Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, England |
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Abstract: | We use the complex and quaternionic hyperbolic versions of Jørgensen's inequality to construct embedded collars about short, simple, closed geodesics in complex and quaternionic hyperbolic manifolds. In general, the width of these collars depend both on the length of the geodesic and on the rotational part of the group element uniformising it. For complex hyperbolic space we are able to use a lemma of Zagier to give an estimate based only on the length. We show that these canonical collars are disjoint from each other and from canonical cusps. We also calculate the volumes of these collars. |
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Keywords: | collars complex hyperbolic manifold Jø rgensen's inequality quaternionic hyperbolic manifold |
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