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The co-surface graph and the geometry of hyperbolic free group extensions

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摘要

We introduce the co-surface graph CS of a finitely generated free group F and use it to study the geometry of hyperbolic group extensions of F. Among other things, we show that the Gromov boundary of the co-surface graph is equivariantly homeomorphic to the space of free arational F-trees and use this to prove that a finitely generated subgroup of Out(F) quasi-isometrically embeds into the co-surface graph if and only if it is purely atoroidal and quasi-isometrically embeds into the free factor complex. This answers a question of I. Kapovich. Our earlier work S. Dowdall and S. J. Taylor, 'Hyperbolic extensions of free groups', to appear in Geom. Topol. shows that every such group gives rise to a hyperbolic extension of F, and here we prove a converse to this result that characterizes the hyperbolic extensions of F arising in this manner. As an application of our techniques, we additionally obtain a Scott-Swarup type theorem for this class of extensions.

著录项

  • 来源
    《Journal of topology》 |2017年第2期|447-482|共36页
  • 作者单位

    Vanderbilt Univ, Dept Math, Stevenson Ctr 1326, Nashville, TN 37240 USA;

    Yale Univ, Dept Math, 10 Hillhouse Ave, New Haven, CT 06520 USA;

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  • 原文格式 PDF
  • 正文语种 英语
  • 中图分类 几何、拓扑;
  • 关键词

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