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Sphere paths in outer space

Camille Horbez
Algebraic & Geometric Topology 12 (2012) 2493–2517
DOI: 10.2140/agt.2012.12.2493
Abstract

We give estimates on the length of paths defined in the sphere model of outer space using a surgery process, and show that they make definite progress in some sense when they remain in some thick part of outer space. To do so, we relate the Lipschitz metric on outer space to a notion of intersection numbers.

Keywords
Outer space, Lipschitz metric, Intersection numbers
Mathematical Subject Classification 2010
Primary: 20F65
References
Publication
Received: 24 June 2012
Revised: 3 November 2012
Accepted: 6 August 2012
Published: 31 January 2013
Authors
Camille Horbez
Ecole Normale Supérieure
45 rue d’Ulm
F-75005 Paris
France