In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004. Atiyah was born...

University of California, Berkeley. Singer is noted for his work with Michael Atiyah, proving the Atiyah–Singer index theorem in 1962, which paved the way for...

proved the theorem in full generality connecting global topology with local geometry. The Riemann–Roch theorem and the Atiyah–Singer index theorem are other...

a whole series of theorems (e.g. Atiyah–Singer index theorem, De Rham's theorem, Grothendieck–Riemann–Roch theorem) establishing deep relationships between...

complexes of sheaves. The theorem has been very influential, not least for the development of the Atiyah–Singer index theorem. Conversely, complex analytic...

the Atiyah–Bott fixed-point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed-point theorem for...

all i. The signature theorem is a special case of the Atiyah–Singer index theorem for the signature operator. The analytic index of the signature operator...

analysis) Trudinger's theorem (functional analysis) Aronszajn–Smith theorem (functional analysis) Atiyah–Singer index theorem (elliptic differential...

essentially all carried out between 1950 and 1960. After that the Atiyah–Singer index theorem opened another route to generalization. Consequently, the Euler...

University of Arkansas Honors College. Chern–Gauss–Bonnet theorem Atiyah–Singer index theorem Chern, Shiing-Shen (March 4, 1998). "Interview with Shiing-Shen...

deduced from the Atiyah–Singer index theorem: Michael Atiyah and Isadore Singer showed that the  genus is the index of the Atiyah–Singer operator, which...

the quantized theory. The relationship of this anomaly to the Atiyah–Singer index theorem was one of the celebrated achievements of the theory. Technically...

shown by Donaldson that the smooth part is orientable. By the Atiyah–Singer index theorem, one may compute that the dimension of M k − {\displaystyle {\mathcal...

approach include the Grothendieck–Riemann–Roch theorem, Bott periodicity, the Atiyah–Singer index theorem, and the Adams operations. In high energy physics...

abstract theorems from geometry to be used to gain insight, ranging from the Chern–Gauss–Bonnet theorem and the Riemann–Roch theorem to the Atiyah–Singer index...

Kasparov in 1980. It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of...

the Atiyah–Singer index theorem, which showed that the  genus of a spin manifold is equal to the index of its Dirac operator. By combining this index result...

are defined, as exemplified through their application to the Atiyah–Singer index theorem. The heat equation, along with variants thereof, is also important...

equation Singular perturbation Cauchy–Kovalevskaya theorem H-principle Atiyah–Singer index theorem Bäcklund transform Viscosity solution Weak solution...

classifying structures and configurations. Famous results include the Atiyah–Singer index theorem for Dirac operators. Roughly speaking, the symmetries of Minkowski...

Index theory has become a subject on its own only after M. F. Atiyah and I. Singer published their index theorems" Rudin 1991, p. 15 1.18 Theorem Let...

Gilkey. They extensively treated the physical applications of the Atiyah-Singer index theorem and related mathematical results. With Hikaru Kawai, he developed...

In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was...

This effect also occurs in a much deeper result: the Atiyah–Singer index theorem states that the index of certain differential operators can be read off...

theory. They also arise in connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem. If E0, E1, ..., Ek are vector bundles on a...

In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result...

{\displaystyle M\times S^{1}} . These zeroes are counted by the Atiyah–Singer index theorem, which gives the answer h times the second Chern class of the...

spinors have been found to be at the heart of approaches to the Atiyah–Singer index theorem, and to provide constructions in particular for discrete series...

cohomology, Hodge theory, and the Atiyah–Singer index theorem. However, even in more classical contexts, the theorem has inspired a number of developments...