SL(n,Z) cannot act on small spheres

Details SL(n,Z) cannot act on small spheres SL(n,Z) cannot act on small spheres

2006-04-11

arxiv.org/abs/math/0604239v2

Mathematics

Geometric Topology

5 pages; this is a corrected version which will appear in Top. Appl. 2008

Scientific paper

The group SL(n,Z) admits a smooth faithful action on the (n-1)-sphere
S^(n-1), induced from its linear action on euclidean space R^n. We show that,
if m < n-1 and n > 2, any smooth action of SL(n,Z) on a mod 2 homology
m-sphere, and in particular on the m-sphere S^m, is trivial.

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