In the paper we give a partial answer to the following question: Let G be finite group acting smoothly on a compact ( smooth) manifold M, such that for each isotropy subgroup H of G the submanifold M-H fixed by H can be deformed without fixed points; is it true that then M can be deformed without fixed points G-equivariantly? The answer is no, in general. It is yes, for any G-manifold, if and only if G is the direct product of a 2-group and an odd-order group
Ferrario, D. (2000). Equivariant deformations of manifolds and real representations. PACIFIC JOURNAL OF MATHEMATICS, 196(2), 353-368 [10.2140/pjm.2000.196.353].
Equivariant deformations of manifolds and real representations
Ferrario, DL
2000
Abstract
In the paper we give a partial answer to the following question: Let G be finite group acting smoothly on a compact ( smooth) manifold M, such that for each isotropy subgroup H of G the submanifold M-H fixed by H can be deformed without fixed points; is it true that then M can be deformed without fixed points G-equivariantly? The answer is no, in general. It is yes, for any G-manifold, if and only if G is the direct product of a 2-group and an odd-order group
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