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Compatible Trees and Outer Automorphisms of a Free Group

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thesis
posted on 01.11.2017, 00:00 by Edgar Andrew Bering
The analogy among linear groups, mapping class groups, and outer automorphism groups is imperfect. One point of disanalogy is McCarthy's theorem on two-generator subgroups of mapping class groups. The theorem states that for any two mapping classes, appropriate powers of the two classes generate either a rank two free group or an abelian group. This statement is false for linear groups, and it is unknown whether or not an analogous statement holds for the outer automorphism group. In this work we prove an analogous statement for linearly growing outer automorphisms, developing a general theory of compatibility for R-tree actions along the way.

History

Advisor

Culler, Marc E

Chair

Culler, Marc E

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Groves, Daniel Shalen, Peter B Whyte, Kevin M Mosher, Lee

Submitted date

August 2017

Issue date

03/07/2017