Raoul Bott: Collected Papers pp 619-627 | Cite as

# [123] Report on the Fixed Point Formula, Séminaire N. Bourbaki

## Introduction

The work to be reported on concerns a generalization of the Lefschetz theorem for elliptic complexes. As Michael Atiyah and I have - alas – already reported on the applications of this extension in various places {(ll 1 [2), …) I will here principally discuss one of our methods of proof which by nov has become nearly embarrassingly transparent. It is also clear that special instances of ou.r procedure abound in the literature , and every lecture seems to uncover new ones. As far as applications go , let me remark though that during the recent visit of F. Hirzebruch at Oxford we seem to have been able to derive the recent results of Langlands {~5)) along a road suggested by Borel some time ago from a generalized form of the fixed point theorem, and the proportionality principle of Hirzebruch.

The question is the following one. We are given a compact smooth manifold X, a sequence of smooth vector bundles \({\rm E}\, = \,\left\{ {{{\rm E}_{\rm{i}}}} \right\}\,,\,{\rm{i =...

## References

- M,F, ATIYAH and R. BOTT, “llotes on the Letschetz fixed point theorem for elliptic complexes”, Harvard Notes, Fall 1964 - soon available.Google Scholar
- M,F, ATIYAH and R, BOTT. Bulletin Note, soon to appear.Google Scholar
- MINAKSHI SUNDRAM and D,A, PLEJEL, Sane properties of Eigenfunctions... , Canadian J, Math, 1949, PP. 242- 255e.Google Scholar
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