TL;DR
The Atiyah-Singer index theorem connects analysis, geometry, and topology, providing a profound mathematical result with broad implications across these fields since the 1960s.
Contribution
This paper reviews the historical development, various formulations, and implications of the Atiyah-Singer index theorem, highlighting its foundational role in mathematics.
Findings
Unified framework linking analysis, geometry, and topology
Multiple formulations of the index theorem
Implications extending to modern mathematics
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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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology