Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T20:17:50.763Z Has data issue: false hasContentIssue false
  • English
  • Français

The Eta Invariant and Non-Singular Bilinear Products on Rn

Published online by Cambridge University Press:  20 November 2018

Peter B. Gilkey
Peter B. Gilkey*
Affiliation:
University of Oregon Eugene, Oregon 97403
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.

Milnor showed that non-singular bilinear products on Rn exist only if n = 1, 2, 4, 8 using topological methods. In this note, we give a proof of this result by purely analytical methods.

Keywords

58G12Eta InvariantPinccomplexnon-singular bilinear forms
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 147 - 154
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Atiyah, M.F., Singer, I.M., and Patodi, V.K.. Spectral asymmetry and Riemannian geometry I. Math. Proc. Camb. Phil. Sioc. 77 (1975), pp. 43–69; II, 78 (1975), pp. 405-432; III, 79 (1976), pp. 71-99.Google Scholar
2. Bahri, A. and Gilkey, P.B.. The eta invariant Pinc bordism and equivariant Spinc bordism for cyclic 2-groups, to appear in Pacific J. Math.Google Scholar
3. Bott, R. and Milnor, J.. On the parallelizability of the spheres, Bulletin of the American Mathematical Society 64(1958), pp. 87–89.Google Scholar
4. Gilkey, P.B.. Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Publish or Perish (1985).Google Scholar
5. Seeley, R.T., Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1967), pp. 288–307.Google Scholar