Almost convex groups and the eight geometries |
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Authors: | Michael Shapiro Melanie Stein |
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Affiliation: | (1) University of Melbourne, 3052 Parkville, VIC, Australia;(2) Ohio State University, 43210 Columbus, OH, USA |
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Abstract: | IfM is a closed Nil geometry 3-manifold then 1(M) is almost convex with respect to a fairly simple geometric generating set. IfG is a central extension or a extension of a word hyperbolic group, thenG is also almost convex with respect to some generating set. Combining these with previously known results shows that ifM is a closed 3-manifold with one of Thurston's eight geometries, 1(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol. |
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Keywords: | 20F32 20F10 20F18 03D40 51H25 53A35 |
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