Skip to main content Accessibility help
×
Home

Metrics of Positive Scalar Curvature on Spherical Space Forms

  • Boris Botvinnik (a1) and Peter B. Gilkey (a2)

Abstract

We use the eta invariant to show every non-simply connected spherical space form of dimension m ≥ 5 has a countable family of non bordant metrics of positive scalar curvature.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Metrics of Positive Scalar Curvature on Spherical Space Forms
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Metrics of Positive Scalar Curvature on Spherical Space Forms
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Metrics of Positive Scalar Curvature on Spherical Space Forms
      Available formats
      ×

Copyright

References

Hide All
1. Atiyah, M.F., Patodi, V.K., and Singer, I.M., Spectral asymmetry and Riemannian geometry, Bull. London Math. Soc. 5(1973), 229234. Spectral asymmetry and Riemannian geometry I, II, III, Math. Proc. Cambridge Philos. Soc. 77(1975), 4369. 78(1975), 405432. 79(1976), 7199.
2. Botvinnik, B. and Gilkey, P., The eta invariant and metrics of positive scalar curvature, Math. Anal., 302(1995), 507517.
3. Botvinnik, B., Gilkey, P., and Stolz, S., The Gromov-Lawson-Rosenberg conjecture for groups periodic cohomology, Inst. Hautes Etudes Sci. Publ. Math. 62(1994), preprint.
4. Donnelly, H., Eta invariants for G spaces, Indiana Univ. Math. J. 27(1978), 889918.
5. Gajer, P., Riemannian metrics of positive scalar curvature on compact manifolds with boundary, Ann. Global Anal. Geom. 5(1987), 179191.
6. Giambalvo, V., pin and pin7 cobordism, Proc. Amer. Math. Soc. 39(1973), 395401.
7. Gilkey, P., The Geometry of Spherical Space Form Groups, Series in Pure Math. 7, World Scientific Press, 1989.
8. Gilkey, P., Invariance Theory, the heat equation, and the Atiyah-Singer index theorem, 2 n d Ed, CRC press, 1995.
9. Gilkey, P., The eta invariant for even dimensional pinc manifolds, Adv. in Math. 58(1985), 243—284.
10. Gromov, M. and Lawson, H.B., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111(1980), 423434. see also Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Etudes Sci. Publ. Math. 58(1983), 83—196.
11. Hitchin, N., Harmonic spinors, Adv. in Math. 14(1974), 1—55.
12. Kreck, M. and Stolz, S., Nonconnected moduli spaces of positive sectional curvature metric, J. Amer. Math. Soc. 6(1993), 825850.
13. Lichnerowicz, A., Spineurs harmoniques, C. R. Acad. Sci. Paris 257(1963), 79.
14. Miyazaki, T., On the existence of positive curvature metrics on non simply connected manifolds, J. Fac. Sci. Univ. Tokyo Sect IA Math. 30(1984), 549561.
15. Rosenberg, J., C* algebras, positive scalar curvature, and the Novikov conjecture, II. In: Geometric Methods in Operator Algebras, Pitman Res. Notes 123, 341—374, Longman Sci. Techn., Harlow, 1986.
16. Rosenberg, J. and Stolz, S., Manifolds of positive scalar curvature. In: Algebraic topology and its applications, (eds. Carlson, G.E., Cohen, R.L., Hsiang, W.C., and Jones, J.D.S.), Springer Verlag, 1994.241-267.
17. Schoen, R. and Yau, S.T., The structure of manifolds with positive scalar curvature, Manuscripta Math. 28(1979), 159183.
18. Stolz, S., Concordance classes of positive scalar curvature metrics, in preparation.
19. Wolf, J., Spaces of constant curvature (5th ed.). Publish or Perish Press, Wilmington, 1985.
20. Wimp, J., Associated Jacobi polynomials and some applications, Canad. J. Math. 39(1987), 983—1000.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Metrics of Positive Scalar Curvature on Spherical Space Forms

  • Boris Botvinnik (a1) and Peter B. Gilkey (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed