Abstract:We prove that the simplicial complex whose simplices are the nonempty partial bases of Fn is homotopy equivalent to a wedge of (n−1)‐spheres. Moreover, we show that it is Cohen–Macaulay.
Answering a question of Hatcher and Vogtmann, we prove that the top homology group of the free factor complex is not the dualizing module for $\operatorname {Aut}(F_{n})$, at least for $n = 5$.
Answering a question of Hatcher and Vogtmann, we prove that the top homology group of the free factor complex is not the dualizing module for $\operatorname {Aut}(F_{n})$, at least for $n = 5$.
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