Index of Elliptic Operators

By Vitaly Volpert. 2011

615 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8872155e910e50604cda85777db85eea204e7a20

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Additivity and non-additivity for perverse signatures (2009, background): “These include cobordism invariance [48], equality to the index of the signature operator and to the L-genus [33], and Novikov additivity [3].”
Twisted K-Homology and Group-Valued Moment Maps (2010, background): “The proof is a straightforward modification of the argument in [9]: One first argues that if H is a closed subgroup of G with t 6∈ H, thenKG • (G/H,A)(t) = 0 for any G-DD bundleA → G/H.”
Fermion Path Integrals And Topological Phases (2015, methodology): “This is not surprising, since the free fermion phases can be classified via K-theory [10] (or by classes of matrices, which are related [11]), and index theory was invented [12,13] as the analysis associated to K-theory.”
Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals (2015, methodology): “Due to the Atiyah-Singer index theorem [216], the la tter is a topological invariant.”
The Dirac Spectrum (2009, methodology): “Vanishing theorems can also be obtained combining the Schrödinger-Lichnerowicz formula with the celebrated AtiyahSinger index theorem [31], stating that the topological and the analytical index of any elliptic linear differential operator coincide.”
Infinite loop spaces and positive scalar curvature (2014, methodology): “Hitchin uses the real family index theorem [8] to compute the index of the family (Dx,v)(x,v)∈X×Rd,0 .”
Symplectic involutions of holomorphic symplectic four‐folds (2010, methodology): “Let us briefly recall the Holomorphic Lefschetz theorem by Atiyah-Singer (see [1]), following the paper by Donovan [8], where the reader can find all the details and the proofs that we are skipping.”
New invariants of G2–structures (2012, background): “diﬀerence D(ϕ,ϕ′) ∈ Zfrom Lemma 1.4. A homotopy of G2-structures is equivalent to a path of non-vanishing spinor ﬁelds. Any path of spinor ﬁelds on Mcan be identiﬁed with a positive spinor ﬁeld son M×[0,1]. We can always ﬁnd s such that the restrictions to M×{1} and M×{0} are the non-vanishing spino”
Nilpotence and descent in equivariant stable homotopy theory (2015, methodology): “Indeed, the pull-back map K̃U 0 G(F τ ) → K̃U 0 G(SR) is given by the analytic index by the Atiyah–Singer index theorem [5].”
Positive scalar curvature on foliations (2015, methodology): “Moreover, by the Atiyah-Singer index theorem [1] (cf.”