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Local topological
properties of asymptotic cones of groups
Gregory R Conner and Curtis Kent |
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Algebraic & Geometric Topology 14 (2014) 1413–1439
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Abstract |
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We define a local analogue to Gromov’s loop division property which we use to give a sufficient condition for an asymptotic cone of a complete geodesic metric space to have uncountable fundamental group. When considering groups our condition allows us to relate the local connectedness properties of the asymptotic cone with combinatorial properties of the group. This is used to understand the asymptotic cones of many groups actively being studied in the literature. |
Keywords
asymptotic cones, fundamental group, loop division property
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F69
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References |
Publication
Received: 16 October 2012
Revised: 1 August 2013
Accepted: 1 August 2013
Published: 7 April 2014
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Authors |
| Gregory R Conner | |
| Department of Mathematics Brigham Young University 275 TMCB Provo, UT 84602 USA |
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| http://www.math.byu.edu/~conner/ | |
| Curtis Kent | |
| Mathematics Department University of Toronto 40 St. George Street Room 6290 Toronto ON M5S 2E4 Canada |
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| http://www.math.toronto.edu/cms/kent-curt/ | |
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