Volume 18, issue 5 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature

Takuro Mochizuki

Geometry & Topology 18 (2014) 2823–2949
Abstract

We study the asymptotic behaviour of doubly periodic instantons with square-integrable curvature. Then we establish an equivalence given by the Nahm transform between the doubly periodic instantons with square integrable curvature and wild harmonic bundles on the dual torus. We also introduce algebraic Nahm transforms, which describe the transformations of the underlying filtered objects.

Dedicated to Professor Shigeru Mukai on the occasion of his 60th birthday

Keywords
instanton, asymptotic behaviour, Nahm transform, harmonic bundle
Mathematical Subject Classification 2010
Primary: 53C07
Secondary: 14J60
References
Publication
Received: 17 March 2013
Revised: 5 November 2013
Accepted: 11 March 2014
Published: 1 December 2014
Proposed: Simon Donaldson
Seconded: Tomasz Mrowka, Richard Thomas
Authors
Takuro Mochizuki
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan