The free factor complex and the dualizing module for the automorphism group of a free group
Zachary Himes, Jeremy Miller, Sam Nariman, and Andrew Putman
TL;DR
This paper investigates the top homology of the free factor complex and its relation to the dualizing module for automorphism groups of free groups, providing a specific counterexample for n=5.
Contribution
It answers a question by Hatcher-Vogtmann by showing the top homology is not the dualizing module for Aut(F_n) when n=5.
Findings
Top homology of the free factor complex is not the dualizing module for Aut(F_5)
Provides a counterexample to a conjecture for n=5
Clarifies the relationship between homology and dualizing modules in this context
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 , at least for .
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory