Atiyah and Singer: the index of elliptic operators on compact manifolds

What changed

Announced a general formula identifying the analytical index of an elliptic operator on a compact oriented differentiable manifold with a topological expression, encompassing major special cases.

Scientific scope

The record is the exact 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications remain separate.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact 1963 Bulletin of the AMS paper. The detailed 1968 proof series, equivariant and family index theorems, boundary cases and later applications remain separate.

Contributors

• M. F. Atiyah · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• I. M. Singer · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• AMS copy of the Atiyah–Singer compact-manifold paper
• Crossref record for the Atiyah–Singer paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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