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

Brück, Benjamin; Gupta, Radhika

Research article (journal) | Peer reviewed

Abstract

Abstract 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.

Details about the publication

JournalProceedings of the London Mathematical Society (Proc. Lond. Math. Soc.)
Volume121
Issue6
Page range1737-1765
StatusPublished
Release year2020
DOI10.1112/plms.12381
Keywords20F65 (primary); 20F28; 20E05; 57M07 (secondary)

Authors from the University of Münster

Brück, Benjamin
Institute of Mathematical Logic and Basic Research