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Homotopy rigidity for Grassmannians
Author:
Allen Back
Journal:
Proc. Amer. Math. Soc. 80 (1980), 327-332
MSC:
Primary 57S25; Secondary 57S15, 57T15
MathSciNet review:
577768
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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.
- [1]
Arunas
Liulevicius, Characters do not lie, Transformation groups
(Proc. Conf., Univ. Newcastle upon Tyne, Newcastle upon Tyne, 1976),
Cambridge Univ. Press, Cambridge, 1977, pp. 139–146. London
Math. Soc. Lecture Note Series, No. 26. MR 0474343
(57 #13989)
- [2]
Arunas
Liulevicius, Homotopy rigidity of linear actions:
characters tell all, Bull. Amer. Math. Soc.
84 (1978), no. 2,
213–221. MR
475124 (81f:57040), http://dx.doi.org/10.1090/S0002-9904-1978-14457-7
- [3]
-, Flag manifolds and homotopy rigidity of linear actions, Proc. Canad. Conf. at the Univ. of British Columbia, August 1977.
- [4]
Arunas Liulevicius and John Ewing, Homotopy rigidity of linear actions on friendly homogeneous spaces (to appear).
- [5]
Wu-yi
Hsiang, Cohomology theory of topological transformation
groups, Springer-Verlag, New York, 1975. Ergebnisse der Mathematik und
ihrer Grenzgebiete, Band 85. MR 0423384
(54 #11363)
- [6]
Allen Back, Involutions of Grassmann manifolds, Thesis, Univ. of California, Berkeley, 1977.
- [7]
L. O'Neill, The fixed point property for Grassmann manifolds, Ph.D. Dissertation, Ohio State Univ., 1974.
- [8]
Henry
Glover and Bill
Homer, Endomorphisms of the cohomology ring of finite Grassmann
manifolds, Geometric applications of homotopy theory (Proc. Conf.,
Evanston, Ill., 1977), I, Lecture Notes in Math., vol. 657, Springer,
Berlin, 1978, pp. 170–193. MR 513548
(80e:55003)
- [9]
Stephen Brewster, Automorphisms of the cohomology ring of finite Grassmann manifolds, Dissertation, Ohio State Univ., 1978.
- [1]
- Anunas Liulevicius, Characters do not lie, Transformation Groups (Ed., Czes Kosniowski), Proc. Conf. on Transformation Groups (Newcastle upon Tyne, August 1976), Cambridge University Press, London and New York, 1976, pp. 139-146. MR 0474343 (57:13989)
- [2]
- -, Homotopy rigidity of linear actions: characters tell all, Bull. Amer. Math. Soc. 84 (1977), 213-221. MR 475124 (81f:57040)
- [3]
- -, Flag manifolds and homotopy rigidity of linear actions, Proc. Canad. Conf. at the Univ. of British Columbia, August 1977.
- [4]
- Arunas Liulevicius and John Ewing, Homotopy rigidity of linear actions on friendly homogeneous spaces (to appear).
- [5]
- Wu-Yi Hsiang, Cohomology theory of topological transformation groups, Springer-Verlag, New York, 1975. MR 0423384 (54:11363)
- [6]
- Allen Back, Involutions of Grassmann manifolds, Thesis, Univ. of California, Berkeley, 1977.
- [7]
- L. O'Neill, The fixed point property for Grassmann manifolds, Ph.D. Dissertation, Ohio State Univ., 1974.
- [8]
- Henry Glover and Bill Homer, Endomorphisms of the cohomology ring of finite Grassmann manifolds, Proc. Northwestern Univ. Homotopy Theory Conf., March 1977. MR 513548 (80e:55003)
- [9]
- Stephen Brewster, Automorphisms of the cohomology ring of finite Grassmann manifolds, Dissertation, Ohio State Univ., 1978.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1980-0577768-4
PII:
S 0002-9939(1980)0577768-4
Article copyright:
© Copyright 1980 American Mathematical Society
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