Local topological properties of asymptotic cones of groups

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.

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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/

Volume 14, issue 3 (2014)

Gregory R Conner and Curtis Kent

Abstract