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user 1822
25
votes
Is every (finite) group action on R^n by diffeomorphisms conjugate to a linear action?
Yes in dimensions ≤ 2 (classical). Yes in dimension 3 via the Geometrization Conjecture (with much earlier work in special cases). No in higher dimensions, with the simplest examples perhaps being cou …
- 3,376
1
vote
Fixed point set for a subcircle of torus actions
The answer to the last question is "no". There exist smooth actions of non-abelian compact Lie groups on euclidean space with empty fixed point set. See Bredon's book, Introduction to Compact Transfor …
- 3,376