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...

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

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

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

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...

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 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...

{\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...

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

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

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

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...

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

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

an involution. It was introduced by Atiyah (1966), motivated by applications to the Atiyah–Singer index theorem for real elliptic operators. A real space...

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...

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...

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...

The origins of the conjecture go back to Fredholm theory, the Atiyah–Singer index theorem and the interplay of geometry with operator K-theory as expressed...

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...

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...

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...

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...

such as hearing the shape of a drum and some proofs of the Atiyah–Singer index theorem. Infinite dimensional manifolds The definition of a manifold...

structures. It was conceived by Alain Connes who was motivated by the Atiyah-Singer index theorem and sought its extension to 'noncommutative' spaces. Some authors...

analytical results were investigated including the proof of the Atiyah–Singer index theorem. The development of complex geometry was spurred on by parallel...