Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Pseudofree representations and $ 2$-pseudofree actions on spheres


Authors: Erkki Laitinen and Paweł Traczyk
Journal: Proc. Amer. Math. Soc. 97 (1986), 151-157
MSC: Primary 57S17; Secondary 20C15, 57S25
DOI: https://doi.org/10.1090/S0002-9939-1986-0831405-5
MathSciNet review: 831405
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize $ 1$-pseudofree real representations of finite groups. We apply this to show that the representations at fixed points of a $ 2$-pseudofree smooth action of a finite group on a sphere of dimension $ \geqslant 5$ are topologically equivalent. Moreover with one possible exception, the sphere is $ G$-homeomorphic to a linear representation sphere.


References [Enhancements On Off] (What's this?)

  • [1] H. F. Blichfeldt, Finite collineation groups, Univ. of Chicago Press, Chicago, 1917.
  • [2] D. Gorenstein, Finite groups, Harper and Row, New York, 1968. MR 0231903 (38:229)
  • [3] W. C. Hsiang and W. Pardon, Orthogonal transformations for which topological equivalence implies linear equivalence, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 459-461. MR 648535 (83g:57010)
  • [4] -, When are topologically equivalent orthogonal transformations linearly equivalent, Invent. Math. 68 (1982), 275-316. MR 666164 (84g:57037)
  • [5] B. Huppert, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften in Einzeldarstellungen, Band 134, Springer-Verlag, Berlin, 1967. MR 0224703 (37:302)
  • [6] S. Illman, Representations at fixed points of actions of finite groups on spheres, Canad. Math. Soc. Conf. Proc., vol. 2, Part 2, Amer. Math. Soc., Providence, R. I., 1982, pp. 135-155. MR 686142 (84b:57031)
  • [7] J. McKay, The non abelian simple groups $ G,\;\left\vert G \right\vert < {10^6}$: Character tables, Comm. Algebra 7 (1979), 1407-1445. MR 539357 (80e:20024)
  • [8] J. H. Lindsey, Complex linear groups of degree six, Canad. J. Math. 23 (1971), 771-790. MR 0289665 (44:6853)
  • [9] I. Madsen and M. Rothenberg, Classifying $ G$-spheres, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 223-226. MR 656199 (83h:57054)
  • [10] T. Petrie, Pseudoequivalence of $ G$-manifolds, Proc. Sympos. Pure Math., vol. 32, Part 1, Amer. Math. Soc., Providence, R. I., 1978, pp. 169-210. MR 520505 (80e:57039)
  • [11] -, Three theorems in transformation groups, Algebraic Topology (Aarhus 1978, Proceedings), Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin and New York, 1979, pp. 549-572. MR 561238 (82b:57031)
  • [12] J. P. Serre, Représentations linéaires des groupes finis, 2nd éd., Hermann, Paris, 1971.
  • [13] E. Stein, Surgery on products with finite fundamental group, Topology 16 (1977), 473-493. MR 0474336 (57:13982)
  • [14] J. A. Wolf, Spaces of constant curvature, McGraw-Hill, New York, 1967. MR 0217740 (36:829)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57S17, 20C15, 57S25

Retrieve articles in all journals with MSC: 57S17, 20C15, 57S25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831405-5
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society