The road trip property: an aid in classifying groups with quadratic isoperimetric inequalities

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Date
2012
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University of Alabama Libraries
Abstract

A property of geodesic metric spaces, called the road trip property, that generalizes hyperbolic and convex metric spaces is introduced. This property is shown to be invariant under quasi-isometry. Thus, it leads to a geometric property of finitely generated groups, also called the road trip property. The main result is that groups with the road trip property are finitely presented and satisfy a quadratic isoperimetric inequality. Examples of groups with the road trip property include hyperbolic, semihyperbolic, automatic, and CAT(0) groups.

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Electronic Thesis or Dissertation
Keywords
Mathematics
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