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The Atiyah-Singer index theorem

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arxiv 2107.03557 v1 pith:3FHZUQUO submitted 2021-07-08 math.HO math-phmath.APmath.ATmath.DGmath.MP

classification math.HOmath-phmath.APmath.ATmath.DGmath.MP
keywords theorematiyah-singerindexsomeachievementanalysisantecedentsbrings
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Vacancy-Induced Topological Phase Transition via Valley Annihilation in an Anisotropic Honeycomb Lattice

    cond-mat.mes-hall 2026-07 conditional novelty 6.0 of 10

    A single vacancy in an anisotropic honeycomb lattice carries winding number ∓1 below t'/t=2 and exactly 0 at and above t'/t=2, a topological phase transition driven by Dirac-valley annihilation.

  2. Local Defects and the Topology of the Haldane Model

    cond-mat.mes-hall 2026-07 accept novelty 5.0 of 10

    Vacancies in the Haldane model host Z2-protected zero modes when sublattice imbalance is odd, with three signatures that distinguish them from trivial adatom defects.

  3. Engineering Topological Materials

    cond-mat.mes-hall 2025-08 conditional novelty 4.0 of 10

    Localized defects with a designed phase winding can shift a Dirac material into a topological class, e.g. from BDI to BDI or CII, generating zero modes.

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