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Homotopy type of the complex of free factors of a free group

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arxiv 1810.09380 v3 pith:AZH3EROC submitted 2018-10-22 math.GR math.GT

Benjamin Brück , Radhika Gupta This is my paper · ORCID
classification math.GRmath.GT
keywords freecomplexgrouphomotopyequivalentfactorfactorssplitting
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We show that the complex of free factors of a free group of rank n > 1 is homotopy equivalent to a wedge of spheres of dimension n-2. We also prove that for n > 1, the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (n-2)-connected. In addition, we show that for every non-trivial free factor system of a free group, the corresponding relative free splitting complex is contractible.

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  1. The minimally displaced set of an irreducible automorphism is locally finite

    math.GR 2019-08 conditional novelty 6.0 of 10

    The minimally displaced set of an irreducible automorphism with exponential growth is uniformly locally finite in any deformation space of a free splitting.

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