Groups with small Dehn functions and bipartite chord diagrams |
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Authors: | Alexander Yu Ol’shanskii Mark V Sapir |
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Institution: | (1) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA;(2) Department of Higher Algebra, MEHMAT, Moscow State University, Moscow, Russia |
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Abstract: | We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function
n2log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show
that n2log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem.
Both authors were supported in part by the NSF grants DMS 0245600 and DMS 0455881. In addition, the research of the first
author was supported in part by the Russian Fund for Basic Research 05-01-00895, the research of the second author was supported
in part by the NSF grant DMS 9978802 and the US-Israeli BSF grant 1999298.
Received: February 2005; Revision: September 2005; Accepted: September 2005 |
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Keywords: | Dehn function conjugacy problem S-machine chord diagram |
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