A note on subfactor projections

Taylor, Samuel J

doi:10.2140/agt.2014.14.805

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A note on subfactor projections

Samuel J Taylor

Algebraic & Geometric Topology 14 (2014) 805–821

DOI: 10.2140/agt.2014.14.805

Abstract

We extend some results of Bestvina and Feighn [arXiv:1107.3308 (2011)] on subfactor projections to show that the projection of a free factor $B$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>$ to the free factor complex of the free factor $A$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>$ is well defined with uniformly bound diameter, unless either $A$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>$ is contained in $B$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>$ or $A$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>$ and $B$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>$ are vertex stabilizers of a single splitting of $F_{n}$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></math>$ , ie, they are disjoint. These projections are shown to satisfy properties analogous to subsurface projections, and we give as an application a construction of fully irreducible outer automorphisms using the bounded geodesic image theorem.

Keywords

subfactor projections,

Out (F_{n})

$\operatorname{Out}(F_n)$ , fully irreducible automorphisms

Mathematical Subject Classification 2010

Primary: 20F65

Secondary: 57M07

References

Publication

Received: 15 August 2013

Revised: 16 September 2013

Accepted: 16 September 2013

Published: 30 January 2014

Authors

Samuel J Taylor
Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin, TX 78712 USA
http://www.ma.utexas.edu/users/staylor/

Volume 14, issue 2 (2014)