Bounded Surgery and Dihedral Group Actions on Spheres
نویسندگان
چکیده
منابع مشابه
Bounded Surgery and Dihedral Group Actions on Spheres
If a finite group G acts freely and simplicially on a complex homotopy equivalent to a sphere S, then G has periodic Tate cohomology: H (G;Z) ∼= H (G;Z) for all i > 0. Swan proved in [26] that this condition was also sufficient. For free topological actions on S itself, the first additional restriction is: Theorem. [19] A finite dihedral group does not act freely and topologically on S. Milnor’...
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We show that a finite dihedral group does not act pseudofreely and locally linearly on an even-dimensional sphere S, with k > 1. This answers a question of R. S. Kulkarni from 1982.
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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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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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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: Journal of the American Mathematical Society
سال: 1991
ISSN: 0894-0347
DOI: 10.2307/2939256