Skip to main content

On the obstruction group to existence of riemannian metrics of positive scalar curvature

Part of the Lecture Notes in Mathematics book series (LNM,volume 1481)

Keywords

  • Scalar Curvature
  • Fundamental Group
  • Spin Manifold
  • Positive Scalar Curvature
  • Arithmetic Genus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Connes, H. Moscovici: Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Topology 29, 345–388 (1990).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. P. Gajer: Riemannian metrics of positive scalar curvature on compact manifolds with boundary. Ann. Global Anal. Geom. 5, 179–191 (1987).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. M. Gromov, B. Lawson: The classification of simply connected manifolds of positive scalar curvature. Ann. Math. 111, 423–434 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M. Gromov, B. Lawson: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publ. IHES 58, 295–408 (1983).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. B. Hajduk: Metrics of positve scalar curvature on spheres and the Gromov-Lawson conjecture. Math. Ann. 208, 409–415 (1988).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. B. Hajduk: Splitting metrics with positive scalar curvature along submanifolds. (to appear)

    Google Scholar 

  7. M. Hall: The theory of groups. Macmillan. New York 1959.

    MATH  Google Scholar 

  8. N. Hitchin: Harmonic spinors. Adv. Math. 14, 1–55 (1974).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. M. Kreck: Positive scalar curvature, P 2(H) and elliptic homology. 29. Arbeitstagung Bonn, 23.–29. Juni 1990. Preprint Max-Planck-Institut.

    Google Scholar 

  10. S. Kwasik, R. Schulz: Positive scalar curvature and periodic fundamental groups. Comment. Math. Helv. 65, 271–286 (1990).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. A. Lichnerowicz: Sprineurs harmoniques. C.R. Acad. Sci. Paris, 257, 7–9 (1963).

    MathSciNet  MATH  Google Scholar 

  12. J. Milnor: Lectures on Morse theory. Princeton.

    Google Scholar 

  13. J. Milnor: Remarks concerning spin manifolds. A Symposium in Honor of Marston Morse, 55–62. Princeton University Press 1965.

    Google Scholar 

  14. M. Miyazaki: On the existence of positive scalar curvature metrics on non-simply connected manifolds. J. Fac. Sci. Tokyo 30, 549–561 (1984).

    MathSciNet  MATH  Google Scholar 

  15. J. Rosenberg: C*-algebras, positve scalar curvature, and the Novikov conjecture II, Proc. U.S.-Japan Seminar on Geometric Methods in Operator Algebras, Kyoto 1963.

    Google Scholar 

  16. J. Rosenberg: C*-algebras, positive scalar curvature, and the Novikov conjecture III, Topology 25, 319–336 (1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. J. Rosenberg: The KO-assembly map and positive scalar curvature (Preprint, December 1989).

    Google Scholar 

  18. R.M. Schoen: Minimal surfaces and positive scalar curvature. Proceedings of ICM Warszawa 1983, 575–578.

    Google Scholar 

  19. R. Schoen, S.T. Yau: On the structure of manifolds with positive scalar curvature. Manuscr. Math. 28, 159–183 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Hajduk, B. (1991). On the obstruction group to existence of riemannian metrics of positive scalar curvature. In: Ferus, D., Pinkall, U., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 1481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083629

Download citation

  • DOI: https://doi.org/10.1007/BFb0083629

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54728-0

  • Online ISBN: 978-3-540-46445-7

  • eBook Packages: Springer Book Archive