Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye

doi:10.2140/agt.2018.18.1195

Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1195-1204
Number of pages	10
Journal	Algebraic and Geometric Topology
Volume	18
Issue number	2
DOIs	https://doi.org/10.2140/agt.2018.18.1195
Publication status	Published - 12 Mar 2018

Keywords

Euler characteristics
Matrix group actions
Zimmer's program

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10.2140/agt.2018.18.1195

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title = "Euler characteristics and actions of automorphism groups of free groups",

abstract = "Let Mr be a connected orientable manifold with the Euler characteristic χ(M) ≢ 0 mod 6. 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(ℤ)) with n ≥ r + 2 on Mr by homeomorphisms is trivial. This confirms a conjecture related to Zimmer{\textquoteright}s program for these manifolds.",

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N2 - Let Mr be a connected orientable manifold with the Euler characteristic χ(M) ≢ 0 mod 6. 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(ℤ)) with n ≥ r + 2 on Mr by homeomorphisms is trivial. This confirms a conjecture related to Zimmer’s program for these manifolds.

AB - Let Mr be a connected orientable manifold with the Euler characteristic χ(M) ≢ 0 mod 6. 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(ℤ)) with n ≥ r + 2 on Mr by homeomorphisms is trivial. This confirms a conjecture related to Zimmer’s program for these manifolds.

KW - Euler characteristics

KW - Matrix group actions

KW - Zimmer's program

UR - https://www.scopus.com/pages/publications/85044074066

U2 - 10.2140/agt.2018.18.1195

DO - 10.2140/agt.2018.18.1195

M3 - Article

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EP - 1204

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 2

ER -

Euler characteristics and actions of automorphism groups of free groups

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