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

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

2009-03-17

arxiv.org/abs/0903.2946v1

Mathematics

Geometric Topology

6 pages

Scientific paper

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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