TY - JOUR
T1 - Euler characteristics and actions of automorphism groups of free groups
AU - Ye, Shengkui
N1 - Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.
PY - 2018/3/12
Y1 - 2018/3/12
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 - http://www.scopus.com/inward/record.url?scp=85044074066&partnerID=8YFLogxK
U2 - 10.2140/agt.2018.18.1195
DO - 10.2140/agt.2018.18.1195
M3 - Article
AN - SCOPUS:85044074066
SN - 1472-2747
VL - 18
SP - 1195
EP - 1204
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 2
ER -