منابع مشابه
Balanced Splittings of Semi-free Actions on Homotopy Spheres
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 ...
متن کاملThe Existence of Free Metacyclic Actions on Homotopy Spheres
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...
متن کاملDecomposability of Homotopy Lens Spaces and Free Cyclic Group Actions on Homotopy Spheres
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...
متن کاملSome Cyclic Group Actions on Homotopy Spheres
In [4J Orlik defined a free cyclic group action on a homotopy sphere constructed as a Brieskorn manifold and proved the following theorem: THEOREM. Every odd-dimensional homotopy sphere that bounds a para-llelizable manifold admits a free Zp-action for each prime p. On the other hand, it was shown ([3J) that there exists a free Zp-action on a 2n-1 dimensional homotopy sphere so that its orbit s...
متن کاملDifferentiable 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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ژورنال
عنوان ژورنال: Topology
سال: 1968
ISSN: 0040-9383
DOI: 10.1016/0040-9383(86)90011-x