A note on actions of the symplectic group Sp(2g,Z) on homology spheres

2009/03/17 by Zimmermann, Bruno P.
#57M60 #57S25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0903.2946

Abstract

The symplectic group Sp(2g,Z) is a subgroup of the linear group SL(2g,Z) and admits a faithful action on the sphere S^(2g-1), induced from its linear action on Euclidean space R^(2g). Generalizing corresponding results for linear groups, we show that, if m < 2g-1 and g > 2, any continuous action of Sp(2g,Z) on a homology m-sphere, and in particular on S^m, is trivial.

Related

• SL(n,Z) cannot act on small spheres
• Actions of SL(n,Z) on homology spheres
• On finite simple groups acting on homology spheres
• On minimal actions of linear fractional and finite simple groups on homology spheres
• Actions of arithmetic groups on homology spheres and acyclic homology manifolds