Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-31T23:56:23.003Z Has data issue: false hasContentIssue false
  • English
  • Français

Twistor spaces and the adiabatic limits of Dirac operators

Published online by Cambridge University Press:  22 January 2016

Masayoshi Nagase
Masayoshi Nagase*
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, Saitama, Saitama 338-8570, Japan, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that a (Spinq-style) twistor space admits a canonical Spin structure. The adiabatic limits of η-invariants of the associated Dirac operator and of an intrinsically twisted Dirac operator are then investigated.

Keywords

57R1581R2553C27
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 164 , December 2001 , pp. 53 - 73
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

[1] Atiyah, M. F., Patodi, V. K. and Singer, I. M., Spectral asymmetry and Riemannian geometry I, Math. Proc. Cambridge Philos. Soc., 77 (1975), 43–69.Google Scholar
[2] Bär, C., Elliptische Operatoren und Darstellungstheorie kompakter Gruppen, Bonner Mathematische Schriften, 248 (1993).Google Scholar
[3] Berline, N., Getzler, E. and Vergne, M., Heat kernels and Dirac operators, Springer-Verlag, Berlin Heidelberg, 1992.Google Scholar
[4] Besse, A. L., Einstein manifolds, Springer-Verlag, Berlin Heidelberg, 1987.Google Scholar
[5] Bismut, J.-M. and Cheeger, J., η-invariants and their adiabatic limits, J. Amer. Math. Soc., 2 (1989), 33–70.Google Scholar
[6] Bismut, J.-M. and Freed, D. S., The analysis of elliptic families II, Dirac operators, eta invariants and the holonomy theorem, Comm. Math. Phys., 107 (1986), 103–163.CrossRefGoogle Scholar
[7] Cheeger, J., On the formulas of Atiyah-Patodi-Singer and Witten, Proc. of ICM, Berkeley (1986), 515–521.Google Scholar
[8] Cheeger, J., η-invariants, the adiabatic approximation and conical singularities, J. Diff. Geometry, 26 (1987), 175–221.Google Scholar
[9] Dai, X., Adiabatic limits, nonmultiplicativity of signature, and Leray spectral sequence, J. Amer. Math. Soc., 4 (1991), 265–321.Google Scholar
[10] Griffiths, P. and Harris, J., Principles of algebraic geometry, John Wiley & Sons, 1978.Google Scholar
[11] Lawson, H. B. and Michelsohn, M., Spin geometry, Princeton Univ. Press, 1989.Google Scholar
[12] Nagase, M., Spinq structures, J. Math. Soc. Japan, 47 (1995), 93–119.Google Scholar
[13] Nagase, M., Quaternionic symplectic manifolds and canonical quantum bundles, J. Math. Sci. Univ. Tokyo, 2 (1995), 347–374.Google Scholar
[14] Nagase, M., Spinq, twistor and Spinc , Comm. Math. Phys., 189 (1997), 107–126.CrossRefGoogle Scholar
[15] O’Brian, N. R. and Rawnsley, J. H., Twistor spaces,, Ann. Global Anal. Geom., 3 (1985), 29–58.Google Scholar
[16] Salamon, S. M., Quaternionic Kähler manifolds, Invent. Math., 67 (1982), 143–171.CrossRefGoogle Scholar
[17] Salamon, S. M., Riemannian geometry and holonomy groups,, Longman Scientific & Technical, 1989.Google Scholar
[18] Witten, E., Global gravitational anomalies, Comm. Math. Phys., 100 (1985), 197–229.CrossRefGoogle Scholar