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The cohomology of an isospectral flow
Author:
David Fried
Journal:
Proc. Amer. Math. Soc. 98 (1986), 363-368
MSC:
Primary 58F19; Secondary 57R19, 58F09, 58F25
MathSciNet review:
854048
Full-text PDF Free Access
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Abstract: Building on work of Tomei, we compute the cohomology of the manifold of real symmetric tridiagonal matrices with distinct fixed eigenvalues. The proof uses the global dynamical properties of the Toda flow on this isospectral manifold.
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Bott and Hans
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spaces, Amer. J. Math. 80 (1958), 964–1029. MR 0105694
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W. Davis, Some aspherical manifolds, Duke Math. J.
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Carlos
Tomei, The topology of isospectral manifolds of tridiagonal
matrices, Duke Math. J. 51 (1984), no. 4,
981–996. MR
771391 (86d:58091), http://dx.doi.org/10.1215/S0012-7094-84-05144-5
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- A. Borel, Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115-207. MR 0051508 (14:490e)
- [BS]
- R. Bott and H. Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964-1029. MR 0105694 (21:4430)
- [D1]
- M. Davis, Some aspherical manifolds, Ohio State Univ., preprint. MR 883666 (88j:57044)
- [D2]
- -, The homology of a space on which a reflection group acts, Ohio State Univ., preprint.
- [G]
- Marvin Greenburg, Lectures on algebraic topology, Benjamin, New York, 1967. MR 0215295 (35:6137)
- [HPT]
- W. Y. Hsiang, R. Palais and C. L. Terng, Geometry and topology of isoparametric submanifolds in Euclidean spaces, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), 4863-4865. MR 799109 (86j:53082)
- [M]
- Jurgen Moser, Finitely many mass points on the line under the influence of an exponential potential--an integrable system, Lecture Notes in Phys., vol. 38, Springer-Verlag, Berlin and New York, 1975, pp. 467-497. MR 0455038 (56:13279)
- [S]
- Steve Smale, The
 -stability theorem, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc, Providence, R. I., 1968, pp. 289-298. MR 0271971 (42:6852)
- [T]
- Carlos Tomei, The topology of isospectral manifolds of tridiagonal matrices, Duke Math. J. 51 (1984), 981-996. MR 771391 (86d:58091)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0854048-6
PII:
S 0002-9939(1986)0854048-6
Article copyright:
© Copyright 1986 American Mathematical Society
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