ASD moduli spaces over four-manifolds with tree-like ends

Kato, Tsuyoshi

doi:10.2140/gt.2004.8.779

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ASD moduli spaces over four-manifolds with tree-like ends

Tsuyoshi Kato

Geometry & Topology 8 (2004) 779–830

DOI: 10.2140/gt.2004.8.779

arXiv: math.GT/0405443

Abstract

In this paper we construct Riemannian metrics and weight functions over Casson handles. We show that the corresponding Atiyah–Hitchin–Singer complexes are Fredholm for some class of Casson handles of bounded type. Using these, the Yang–Mills moduli spaces are constructed as finite dimensional smooth manifolds over Casson handles in the class.

Keywords

Yang–Mills theory, Casson handles

Mathematical Subject Classification 2000

Primary: 57M30, 57R57

Secondary: 14J80

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Publication

Received: 16 October 2001

Revised: 29 March 2004

Accepted: 29 April 2004

Published: 20 May 2004

Proposed: Simon Donaldson

Seconded: Ronald Stern, Robion Kirby

Authors

Tsuyoshi Kato
Department of Mathematics Kyoto University Kyoto 606-8502 Japan

Volume 8, issue 2 (2004)