The Atiyah Singer index theorem : an introduction / by 268006 Shanahan, Patrick

Necessary and sufficient conditions for the validity of Luttinger’s theorem by Joshuah T Heath, Kevin S Bedell

“…In this paper, we propose the minimal requirements for the application of a hard Luttinger’s theorem to a generic fermionic system of arbitrary interaction strength by invoking the Atiyah–Singer index theorem to quantify the topologically-robust behavior of a generalized Fermi surface. …”
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Index theorems and magnetic monopoles on asymptotically conic manifolds by Kottke, Christopher N. (Christopher Nicholas)

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Verification & discretization of the index theorem for a two dimensional dirac operator by Lim, Kim Song

“…The famous Atiyah-Singer Index Theorem states that for an elliptic partial differential operator D on a compact manifold, the analytical index (related to the solution space of the partial differential equation Df = 0) is equal to the topological index (defined in terms of some topological data of D). …”
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Gravitational anomalies of fermionic higher-spin fields by Victor Lekeu, Yi Zhang

“…Abstract Using the Atiyah-Singer index theorem, we formally compute gravitational anomalies for fermionic higher-spin fields in two, six and ten dimensions, as well as the U(1) mixed gauge-gravitational anomaly in four dimensions. …”
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Influence of topology on fermionic zero-modes in lattice gauge theory by Petrashyk, Andriy

“…The staggered fermion index obtained is shown to be determined by the underlying gauge field topology in accordance with the Atiyah-Singer Index theorem. It is also found to perform as well as the Wilson index, while being computationally more efficient.…”
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Index of lattice dirac operators by Reetabrata Har

“…The general topic of this thesis is how to define and compute the index of discretised “lattice” versions of the Dirac operator coupled to a topologically nontrivial gauge field. The famous Atiyah-Singer Index Theorem, applied to the usual continuum Dirac operator, says that its index is equal to the topological charge of the gauge field. …”
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Anomaly constraints and string/F-theory geometry in 6D quantum gravity by Taylor, Washington

“…Quantum anomalies, determined by the Atiyah-Singer in- dex theorem, place strong constraints on the space of quantu m gravity theories in six dimensions with minimal supersymmetry. …”
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