Tame combing and almost convexity conditions |
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Authors: | Sean Cleary Susan Hermiller Melanie Stein Jennifer Taback |
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Institution: | 1. Department of Mathematics, The City College of New York, The City University of New York, New York, NY, 10031, USA 2. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588, USA 3. Department of Mathematics, Trinity College, Hartford, CT, 06106, USA 4. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011, USA
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Abstract: | We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we explicitly construct such combings for Thompson??s group F and the Baumslag?CSolitar groups BS(1, p) with p ??? 3. In order to make this construction for Thompson??s group F, we significantly expand the understanding of the Cayley complex of this group with respect to the standard finite presentation. In particular we describe a quasigeodesic set of normal forms and combinatorially classify the arrangements of 2-cells adjacent to edges that do not lie on normal form paths. |
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