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Limit groups and Makanin-Razborov diagrams for hyperbolic groups

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ReinfeldtC_0610_macs.pdf (775.7Kb)
Date
2010-06
Author
Reinfeldt, Cornelius
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Abstract
This thesis gives a detailed description of Zlil Sela’s construction of Makanin-Razborov diagrams which describe Hom(G, T), the set of all homomorphisms from G to T, where G is a finitely generated group and T is a hyperbolic group. Moreover, while Sela’s construction requires T to be torsion-free, this thesis removes this condition and addresses the case of arbitrary hyperbolic groups. Sela’s shortening argument, which is the main tool in the construction of the Makanin- Razborov diagrams, relies on the Rips machine, a structure theorem for finitely generated groups acting stably on real trees. As homomorphisms from a f.g. group G to a hyperbolic group T give rise to stable actions of G on real trees, which appear topologically as limits of the G-actions on the Cayley graph of T, the Rips machine and the shortening argument allow us to explore the structure of Hom(G, T) and construct Makanin-Razborov diagrams which encode all homomorphisms from G to T. While Sela’s version of the Rips machine allows the formulation of the shortening argument only in the case where T is torsion-free, Guirardel has presented a generalized version of the Rips machine, which we exploit to generalize the shortening argument and the construction of Makanin-Razborov diagrams to the case of arbitrary hyperbolic groups.
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http://hdl.handle.net/10399/2375
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©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

  • About
  • Copyright
  • Accessibility
  • Policies
  • Privacy & Cookies
  • Feedback
AboutCopyright
AccessibilityPolicies
Privacy & Cookies
Feedback