Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
ASD moduli spaces over four-manifolds with tree-like ends

Tsuyoshi Kato

Geometry & Topology 8 (2004) 779–830

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