Volume 14, issue 3 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Local topological properties of asymptotic cones of groups

Gregory R Conner and Curtis Kent

Algebraic & Geometric Topology 14 (2014) 1413–1439
Abstract

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
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F69
References
Publication
Received: 16 October 2012
Revised: 1 August 2013
Accepted: 1 August 2013
Published: 7 April 2014
Authors
Gregory R Conner
Department of Mathematics
Brigham Young University
275 TMCB
Provo, UT 84602
USA
http://www.math.byu.edu/~conner/
Curtis Kent
Mathematics Department
University of Toronto
40 St. George Street
Room 6290
Toronto ON M5S 2E4
Canada
http://www.math.toronto.edu/cms/kent-curt/