Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature

Mochizuki, Takuro

doi:10.2140/gt.2014.18.2823

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Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature

Takuro Mochizuki

Geometry & Topology 18 (2014) 2823–2949

DOI: 10.2140/gt.2014.18.2823

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

Volume 18, issue 5 (2014)