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

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 Sm, is trivial.

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