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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pseudofree group actions on spheres


Author: Allan L. Edmonds
Journal: Proc. Amer. Math. Soc. 138 (2010), 2203-2208
MSC (2010): Primary 57S25; Secondary 57S17
Published electronically: February 11, 2010
MathSciNet review: 2596060
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Abstract: 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 not act pseudofreely and locally linearly on an actual $ n$-sphere when $ n\equiv 0\mod 4$. It is also shown that the dihedral group does act pseudofreely and locally linearly, with three singular orbits, on an $ n$-manifold when $ n\equiv 2\mod 4$. Orientation-reversing actions are also considered.


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Additional Information

Allan L. Edmonds
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: edmonds@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10339-6
PII: S 0002-9939(10)10339-6
Keywords: Group action, pseudofree, sphere, dihedral group
Received by editor(s): June 19, 2009
Published electronically: February 11, 2010
Dedicated: Dedicated to José María Montesinos on the occasion of his 65th birthday
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.