The Existence of Free Metacyclic Actions on Homotopy Spheres
نویسنده
چکیده
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. The main result of this note is that most metacyclic groups of odd order can act freely and smoothly on some homotopy sphere (Corollary 6). Of independent interest is the discussion of the algebraic tools used in the solution.
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تاریخ انتشار 2007