Volume 18, issue 2 (2018)

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Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye

Algebraic & Geometric Topology 18 (2018) 1195–1204

Let Mr be a connected orientable manifold with the Euler characteristic χ(M)0mod6. Denote by SAut(Fn) the unique subgroup of index two in the automorphism group of a free group. Then any group action of SAut(Fn) (and thus the special linear group SLn()) with n r + 2 on Mr by homeomorphisms is trivial. This confirms a conjecture related to Zimmer’s program for these manifolds.

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Zimmer's program, Euler characteristics, matrix group actions
Mathematical Subject Classification 2010
Primary: 57S20
Secondary: 57S17
Received: 15 August 2017
Revised: 25 September 2017
Accepted: 5 October 2017
Published: 12 March 2018
Shengkui Ye
Department of Mathematical Sciences
Xi’an Jiaotong-Liverpool University