Fixed-point sets of smooth actions on spheres
2007 ◽
Vol 1
(1)
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pp. 95-128
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AbstractGiven a group, it is a basic problem to determine which manifolds can occur as a fixed-point set of a smooth action of this group on a sphere. The current article answers this problem for a family of finite groups including perfect groups and nilpotent Oliver groups. We obtain the answer as an application of a new deleting and inserting theorem which is formulated to delete (or insert) fixed-point sets from (or to) disks with smooth actions of finite groups. One of the keys to the proof is an equivariant interpretation of the surgery theory of S. E. Cappell and J. L. Shaneson, for obtaining homology equivalences.
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2010 ◽
Vol 81
(2)
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pp. 298-303
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1980 ◽
Vol 23
(4)
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pp. 453-455
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1979 ◽
Vol 31
(5)
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pp. 1017-1032
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1985 ◽
Vol 37
(1)
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pp. 17-28
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2014 ◽
Vol 12
(06)
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pp. 1450042
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1994 ◽
Vol 17
(3)
◽
pp. 457-462
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2020 ◽
Vol 29
(04)
◽
pp. 2050021
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