# Atiyah–Bott Fixed-Point Theorem

Tech

## What is Atiyah–Bott fixed-point theorem?

In mathematics, the Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for smooth manifolds M, which uses an elliptic complex on M. This is a system of elliptic differential operators on vector bundles, generalizing the de Rham complex constructed from smooth differential forms which appears in the original Lefschetz fixed-point theorem.

### Technology Types

fixed-point theorempropositionstatementtheoremtheorems in differential topologytheory

### Synonyms

Atiyah-Bott fixed point formulaAtiyah-Bott fixed point theoremAtiyah-Bott fixed-point formulaAtiyah-Bott fixed-point theoremAtiyah-Bott formulaAtiyah–Bott fixed point formulaWoods Hole fixed point theoremWoods Hole fixed-point theoremWoods Hole formula

### Translations

Atiyah-Bott-Fixpunktsatz (de)アティヤ＝ボットの不動点定理 (ja)

## Tech Info

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— Date merged: 11/6/2021, 1:32:52 PM
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