Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T07:55:22.214Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

[1]Berend, D. and G kat Separating topology and number theory in the Atiyah-Singer g-signature formula’, Duke Math J. soc. (1990), 939–971Google Scholar
[2]Bredon, G. E., Introduction to compact transformation groups (Academic Press, London,1972).Google Scholar
[3]Dovermann, K. H. ‘Rigid cyclic group actions on cohomology complex projective spaces’, Math. Proc. Cambridge 101 1987, 487–507.Google Scholar
[4]Dovermann, K. H., masoda, M. and Suh, D. Y., ‘Rigid versus non-rigid cyclic actions’, Comment. Math. Helv 64 (1989), 269–285CrossRefGoogle Scholar
[5]Dovermann, K. H., and Involutions of cohomology complex projective space with codimension Univ. Math. J. 41 (1992), 197–211.Google Scholar
[6]Dovermann, K. H.Space with degree one codimension-two fixed submanifolds’, Pacific J Math. 381–401.Google Scholar
[7]Little, R. D.. ‘projective spaces with divisible splitting invariants’, Pacific J. Math. 140 (1989), 251–252.Google Scholar
[8]Little, R. D., ‘Self-intermanifolds and relations for the multisignature’, Math. Scand. 69 (1991), 167–178.CrossRefGoogle Scholar
[9]Masuda, M., Smooth cohomology complex projective spaces with a fixed point of codimension 2 A Feld of (Academic Press, Boston, 1988), pp. 585–602.Google Scholar
[10]Milnor, J. W. and Scishett, J. D.Characteristic classes, Ann. of Math. Stud. 76 (Princeton Univ. Press, Princeton, 1974).Google Scholar
[11]Sullivan, D., Triangulatine and smoothing homotopy equivalences and homemorphisms Geometric topology seminar notes (Princeton University, Princeton, 1967).Google Scholar
[12]Wall, C. T. C., Surgery on compact manifolds (Academic Press, London, 1970).Google Scholar