| Summary: | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Includes bibliographical references (p. 131-134) and index. === The main result is a computation of the Nahm transform of a SU(2)-instanton over R x 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 R⁴ is given, preceding a description of the heuristic behind the theory of instantons on quotients of R⁴. 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. === by Benoit Charbonneau. === Ph.D.
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