Euler characteristics and actions of automorphism groups of free groups

Ye, Shengkui

doi:10.2140/agt.2018.18.1195

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Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye

Algebraic & Geometric Topology 18 (2018) 1195–1204

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 ${SL}_{n} (ℤ)$ ) with $n \geq r + 2$ on $M^{r}$ by homeomorphisms is trivial. This confirms a conjecture related to Zimmer’s program for these manifolds.

Keywords

Zimmer's program, Euler characteristics, matrix group actions

Mathematical Subject Classification 2010

Primary: 57S20

Secondary: 57S17

References

Publication

Received: 15 August 2017

Revised: 25 September 2017

Accepted: 5 October 2017

Published: 12 March 2018

Authors

Shengkui Ye
Department of Mathematical Sciences Xi’an Jiaotong-Liverpool University Jiangsu China
https://yeshengkui.wordpress.com/

Volume 18, issue 2 (2018)