Geodesic
Local topological properties of asymptotic cones of groups
Conner, Gregory R1 ; Kent, Curtis2
1Department of Mathematics, Brigham Young University, 275 TMCB, Provo, UT 84602, USA
2Mathematics Department, University of Toronto, 40 St. George Street, Room 6290, Toronto ON M5S 2E4, Canada
Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1413-1439
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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.

DOI : 10.2140/agt.2014.14.1413
Classification : 20F65, 20F69
Keywords: asymptotic cones, fundamental group, loop division property

Conner, Gregory R  1   ; Kent, Curtis  2

1 Department of Mathematics, Brigham Young University, 275 TMCB, Provo, UT 84602, USA
2 Mathematics Department, University of Toronto, 40 St. George Street, Room 6290, Toronto ON M5S 2E4, Canada 
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Conner, Gregory R; Kent, Curtis. Local topological properties of asymptotic cones of groups. Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1413-1439. doi: 10.2140/agt.2014.14.1413

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