Free differentiable $S^1$ and $S^3$ actions on homotopy spheres
نویسندگان
چکیده
منابع مشابه
Differentiable Z9 Actions on Homotopy Spheres
The results of [4] proved that many exotic spheres do not admit smooth actions of relatively high-dimensional compact Lie groups (all group actions considered in this paper are assumed to be effective). It was clear that stronger results should hold in certain cases, and this was confirmed in [5]. A notable feature of [5] is the use of nonexistence theorems for certain smooth circle actions to ...
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Introduction. It is shown in [4] that there is an infinite family of semifree Zm actions on odd dimensional homotopy spheres. There is also an infinite family of semifree S actions on odd dimensional homotopy spheres (see [2], [5]). On the other hand, it is announced in [2] that there are only finitely many inequivalent semifree S actions on even dimensional homotopy spheres. Hence it is intere...
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n+k Let 23 be a hornotopy (n+k)-sphere and p : G)< ~E~-2] a smooth semi-free action of a finite group G on 23 with fixed-point set a manifold F n of dimension no A decomposition of 23 into two G-invariant disks will be called a splitting of the action and the induced splitting of 2] G denoted F = FI<9 F 2. We ask whether every such action has a splitting with Hi(F1) ~Hi(F2) for i> 0 (these are ...
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This question is rather old [3]: Which groups having periodic cohomology can act freely on some homotopy sphere? The first nontrivial restriction was supplied by Milnor in [3]. Every element of order two must lie in the center. Swan [ô] showed that any group with periodic cohomology acts freely on a c.w. complex of the homotopy type of sphere. If the group has odd order then it is metacyclic. T...
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Let p be a linear Zn action on C and let p also denote the induced Z„ action on S2p~l x D2q, D2p x S2q~l and S2p~l x S2q~l " 1m_1 where p = [m/2] and q = m — p. A free differentiable Zn action (£ , ju) on a homotopy sphere is p-decomposable if there is an equivariant diffeomorphism of (S2p~l x S2q~l, p) such that (S2m_1, ju) is equivalent to (£(*), ¿(*)) where S(*) = S2p_1 x D2q U^, D2p x S...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1972
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1224