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arXiv · 0903.2946

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

Bruno P. Zimmermann
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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.

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Bruno P. Zimmermann. 2009-03-17. A note on actions of the symplectic group Sp(2g,Z) on homology spheres. https://arxiv.org/abs/0903.2946

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