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Surface Maps into Free Groups


Walker, Alden Kent (2012) Surface Maps into Free Groups. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FDRS-9S44.


We exploit the combinatorial properties of surface maps into free groups to prove several new results in the field of stable commutator length and bounded cohomology. We show that random homomorphisms between free groups are isometries of scl; we prove interesting properties of the scl unit ball; we describe a transfer construction for quasimorphisms and give an infinite family of chains whose scl it certifies; we linearize the dynamics of endomorphisms on free groups and use this to prove that random endomorphisms can be realized by surface immersions, which provides many examples of surface subgroups of HNN extensions of free groups; and finally, we give an algorithm to compute scl in free products of finite or infinite cyclic groups that generalizes and improves previous work.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:stable commutator length, free groups, surface maps
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2012. Scott Russell Johnson Prize for Excellence in Graduate Study in Mathematics, 2011. Apostol Award for Excellence in Teaching in Mathematics, 2010.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Calegari, Danny C.
Thesis Committee:
  • Markovic, Vladimir (chair)
  • Calegari, Danny C.
  • Marcolli, Matilde
  • Graber, Thomas B.
Defense Date:18 May 2012
Non-Caltech Author Email:alden.walker (AT)
Record Number:CaltechTHESIS:05212012-102942842
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7057
Deposited By: Alden Walker
Deposited On:22 May 2012 16:39
Last Modified:28 Oct 2021 19:12

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