Fundamental groups of asymptotic cones |
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Authors: | A Erschler D Osin |
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Institution: | a CNRS, University Lille 1, UFR de Mathématiques, 59655, Villeneuve d’Ascq Cedex, France b Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240-0001, USA |
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Abstract: | We show that for any metric space M satisfying certain natural conditions, there is a finitely generated group G, an ultrafilter ω, and an isometric embedding ι of M to the asymptotic cone Coneω(G) such that the induced homomorphism ι*:π1(M)→π1(Coneω(G)) is injective. In particular, we prove that any countable group can be embedded into a fundamental group of an asymptotic cone of a finitely generated group. |
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Keywords: | 20F69 14F35 20F06 |
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