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Journal of the Australian Mathematical Society - Series A
Vol. 65 Part 1 (1998)

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

Robert D. Little
Department of Mathematics
University of Hawaii at Manoa
Honolulu HI 96822
USA

Abstract:

If M2n is a cohomology $\Bbb CP^n$ and p is an odd prime, let Gp be the cyclic group of order p. A $\op{Type}
II_0$ Gp action on M2n is an action with fixed point set a codimension-2 submanifold and an isolated point. A $\op{Type}
II_0$ 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 $\op{Type}
II_0$, then every $\op{Type}
II_0$ Gp action on M2n is standard and so, if n is odd, $\Bbb CP^n$ admits a Gp action of $\op{Type}
II_0$ if and only if the action is standard.

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© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
1998-09-18