Biomedical subjects
Publications and source records attributed to M F Atiyah.
Characteristic classes for the index of the Dirac family [unk](A) are computed in terms of differential forms on the orbit space of vector potentials under gauge transformations. They represent obstructions to the existence of a covariant Dirac propagator. The first obstruction is related to a chiral anomaly.
The values of 0 of Shimizu L-functions are realized as the signature defects of framed manifolds. This settles a conjecture of Hirzebruch [Hirzebruch, F. (1973) Enseign. Math. 19, 183-281] affirmatively. The proof employs the spectral theory of elliptic operators.
A study is made of the self-dual Yang-Mills fields in Euclidean 4-space. For SU(2) gauge theory it is rigorously shown that the solutions depend on 8k - 3 parameters, where k is the Pontrijagin index.