Analytic aspects of periodic instantons
Abstract (summary)
The main result is a computation of the Nahm transform of a SU(2)-instanton over [special characters omitted] × T3, called spatially-periodic instanton. It is a singular monopole over T3, a solution to the Bogomolny equation, whose rank is computed and behavior at the singular points is understood under certain conditions.
A full description of the Riemannian ADHMN construction of instantons on [special characters omitted] is given, preceding a description of the heuristic behind the theory of instantons on quotients of [special characters omitted]. The Fredholm theory of twisted Dirac operators on cylindrical manifolds is derived, the spectra of spin Dirac operators on spheres and on product manifolds are computed. A brief discussion on the decay of spatially-periodic and doubly-periodic instantons is included. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)