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Regular cyclic actions on complex projective space with codimension-two fixed points

Published online by Cambridge University Press:  09 April 2009

Robert D. Little
Robert D. Little
Affiliation:
Department of Mathematics, University of Hawaii at Manoa, Honolulu HI 96822, USA
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Abstract

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If M2n is a cohomology CPn and P is an odd prime, let Gp be the cyclic group of order p. A Type I I0Gp action on M2n is an action with fixed point set a codimension-2 submanifold and an isolated point. A Type I I0 Gp action is standard if it is regular and the degree of the fixed codimension-2 submanifold is one. If n is odd and M2n admits a standard Gp action of Type I I0, then every Type I I0Gp action M2n is standard and so, if n is odd, CPn admits a Gp action of Type I I0 if and only if the action is standard.

MSC classification

Secondary: 57S17: Finite transformation groups 57S25: Groups acting on specific manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 1 , August 1998 , pp. 51 - 67
Copyright
Copyright © Australian Mathematical Society 1998

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