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We show that the complex of free factors of a free group of rank n >= 2 is homotopy equivalent to a wedge of spheres of dimension n-2. We also prove that for n>=2, 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 spitting complex is contractible. Show more
Journal / seriesProceedings of the London Mathematical Society
Pages / Article No.
Subject20F65 (primary); 20F28; 20F05; 57M07 ( secondary)
Organisational unit08802 - Iozzi, Alessandra (Tit.-Prof.)
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