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The Atiyah–Singer index theorem


Author: Daniel S. Freed
Journal: Bull. Amer. Math. Soc. 58 (2021), 517-566
MSC (2020): Primary 58J20, 58J28, 58J52, 19K56, 81T50
DOI: https://doi.org/10.1090/bull/1747
Published electronically: July 8, 2021
MathSciNet review: 4311554
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Abstract: The Atiyah–Singer index theorem, a landmark achievement of the early 1960s, brings together ideas in analysis, geometry, and topology. We recount some antecedents and motivations, various forms of the theorem, and some of its implications, which extend to the present.


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Additional Information

Daniel S. Freed
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
MR Author ID: 69015
ORCID: 0000-0003-0150-1555
Email: dafr@math.utexas.edu

Received by editor(s): June 10, 2021
Published electronically: July 8, 2021
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant Number DMS-2005286.
Dedicated: In memory of Michael Atiyah
Article copyright: © Copyright 2021 American Mathematical Society