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, for g> 2, any continuous action of Sp(2g,Z) on a homology m-sphere, and in particular on S^m, is trivial if m < 2g-1.
Sp(2g,Z) cannot act on small spheres
ZIMMERMANN, BRUNO
2010-01-01
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, for g> 2, any continuous action of Sp(2g,Z) on a homology m-sphere, and in particular on S^m, is trivial if m < 2g-1.File in questo prodotto:
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