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The Atiyah-Singer index theorem
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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.
Forward citations
Cited by 3 Pith papers
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Vacancy-Induced Topological Phase Transition via Valley Annihilation in an Anisotropic Honeycomb Lattice
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.
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Local Defects and the Topology of the Haldane Model
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.
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Engineering Topological Materials
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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