Pseudofree group actions on spheres
نویسندگان
چکیده
منابع مشابه
Pseudofree Group Actions on Spheres
R. S. Kulkarni showed that a finite group acting pseudofreely, but not freely, preserving orientation, on an even-dimensional sphere (or suitable sphere-like space) is either a periodic group acting semifreely with two fixed points, a dihedral group acting with three singular orbits, or one of the polyhedral groups, occurring only in dimension 2. It is shown here that the dihedral group does no...
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We characterize 1-pseudofree real representations of finite groups. We apply this to show that the representations at fixed points of a 2-pseudofree smooth action of a finite group on a sphere of dimension > 5 are topologically equivalent. Moreover with one possible exception, the sphere is Ghomeomorphic to a linear representation sphere.
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This can be stated in a more symmetric manner. Let r be any positive integer not equal to 3. Then n acts freely and homologically trivially on Z r i ff n acts freely and homologically trivially on SL In fact, there is a one-to-one correspondence between such actions on U and such actions on S r. (The classification of such actions is discussed in w In addition the actions constructed have the p...
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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...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-10-10339-6