The free factor complex and the dualizing module for the automorphism group of a free group

Abstract

Answering a question of Hatcher-Vogtmann, we prove that the top homology group of the free factor complex is not the dualizing module for $\text{Aut}(F_n)$, at least for $n=5$.

arXiv comment30 pages, minor revision; to appear in IMRN

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Cited by in corpus (3)

• Cohen--Macaulay Complexes, Duality Groups, and the dualizing module of $\mathrm{Out}(F_N)$
• Posets arising from decompositions of objects in a monoidal category
• Connectivity of partial basis complexes of freely decomposable groups