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2018 Euler characteristics and actions of automorphism groups of free groups
Shengkui Ye
Algebr. Geom. Topol. 18(2): 1195-1204 (2018). DOI: 10.2140/agt.2018.18.1195

Abstract

Let M r be a connected orientable manifold with the Euler characteristic χ ( M ) 0 mod 6 . Denote by SAut ( F n ) the unique subgroup of index two in the automorphism group of a free group. Then any group action of SAut ( F n ) (and thus the special linear group SL n ( ) ) with n r + 2 on M r by homeomorphisms is trivial. This confirms a conjecture related to Zimmer’s program for these manifolds.

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Shengkui Ye. "Euler characteristics and actions of automorphism groups of free groups." Algebr. Geom. Topol. 18 (2) 1195 - 1204, 2018. https://doi.org/10.2140/agt.2018.18.1195

Information

Received: 15 August 2017; Revised: 25 September 2017; Accepted: 5 October 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859618
MathSciNet: MR3773752
Digital Object Identifier: 10.2140/agt.2018.18.1195

Subjects:
Primary: 57S20
Secondary: 57S17

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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