Algebraic & Geometric Topology

Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye

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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.

Article information

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

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

Permanent link to this document
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

Keywords
Zimmer's program Euler characteristics matrix group actions

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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