## Algebraic & Geometric Topology

### Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye

#### 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 $SL n ( ℤ )$) with $n ≥ r + 2$ on $M r$ by homeomorphisms is trivial. This confirms a conjecture related to Zimmer’s program for these manifolds.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 2 (2018), 1195-1204.

Dates
Revised: 25 September 2017
Accepted: 5 October 2017
First available in Project Euclid: 22 March 2018

https://projecteuclid.org/euclid.agt/1521684034

Digital Object Identifier
doi:10.2140/agt.2018.18.1195

Mathematical Reviews number (MathSciNet)
MR3773752

Zentralblatt MATH identifier
06859618

Subjects
Primary: 57S20: Noncompact Lie groups of transformations
Secondary: 57S17: Finite transformation groups

#### Citation

Ye, Shengkui. Euler characteristics and actions of automorphism groups of free groups. Algebr. Geom. Topol. 18 (2018), no. 2, 1195--1204. doi:10.2140/agt.2018.18.1195. https://projecteuclid.org/euclid.agt/1521684034

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