Hyperbolicity of the complex of free factors
Mladen Bestvina, Mark Feighn
TL;DR
This paper proves that the complex of free factors of a free group is hyperbolic by developing the geometry of folding paths in Outer space, providing new insights into the geometric structure of free groups.
Contribution
It introduces a geometric framework for folding paths in Outer space and establishes the hyperbolicity of the free factor complex, a significant advancement in geometric group theory.
Findings
The free factor complex is hyperbolic.
Folding paths in Outer space have a well-defined geometric structure.
The results have implications for understanding automorphisms of free groups.
Abstract
We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic.
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