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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Homotopy rigidity for Grassmannians
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by Allen Back PDF
Proc. Amer. Math. Soc. 80 (1980), 327-332 Request permission

Abstract:

Two n-dimensional unitary representations which differ by complex conjugation or tensoring with a character induce topologically equivalent actions on the Grassmann manifold of complex m-planes in n-space. This paper shows under modest dimension hypotheses that only such projectively equivalent linear representations of compact connected Lie groups can give topologically conjugate actions.
References
  • Arunas Liulevicius, Characters do not lie, Transformation groups (Proc. Conf., Univ. Newcastle upon Tyne, Newcastle upon Tyne, 1976) London Math. Soc. Lecture Note Series, No. 26, Cambridge Univ. Press, Cambridge, 1977, pp. 139–146. MR 0474343
  • Arunas Liulevicius, Homotopy rigidity of linear actions: characters tell all, Bull. Amer. Math. Soc. 84 (1978), no. 2, 213–221. MR 475124, DOI 10.1090/S0002-9904-1978-14457-7
    • —, Flag manifolds and homotopy rigidity of linear actions, Proc. Canad. Conf. at the Univ. of British Columbia, August 1977. Arunas Liulevicius and John Ewing, Homotopy rigidity of linear actions on friendly homogeneous spaces (to appear).
  • Wu-yi Hsiang, Cohomology theory of topological transformation groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 85, Springer-Verlag, New York-Heidelberg, 1975. MR 0423384
    • Allen Back, Involutions of Grassmann manifolds, Thesis, Univ. of California, Berkeley, 1977. L. O’Neill, The fixed point property for Grassmann manifolds, Ph.D. Dissertation, Ohio State Univ., 1974.
  • Henry Glover and Bill Homer, Endomorphisms of the cohomology ring of finite Grassmann manifolds, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977) Lecture Notes in Math., vol. 657, Springer, Berlin, 1978, pp. 170–193. MR 513548
    • Stephen Brewster, Automorphisms of the cohomology ring of finite Grassmann manifolds, Dissertation, Ohio State Univ., 1978.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 80 (1980), 327-332
  • MSC: Primary 57S25; Secondary 57S15, 57T15
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0577768-4
  • MathSciNet review: 577768