TY  - JOUR
AB  - 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 splitting complex is contractible.
DA  - 2020
DO  - 10.1112/plms.12381
LA  - eng
IS  - 6
M2  - 1737
PY  - 2020
SN  - 0024-6115
SP  - 1737-1765
T2  - Proceedings of the London Mathematical Society
TI  - Homotopy type of the complex of free factors of a free group
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29517296
Y2  - 2024-11-22T08:43:05
ER  -