Geometry & Topology, Vol. 8 (2004) Paper no. 21, pages 779--830.

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

Tsuyoshi Kato

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

AMS subject classification. Primary: 57M30, 57R57. Secondary: 14J80.

DOI: 10.2140/gt.2004.8.779

E-print: arXiv:math.GT/0405443

Submitted to GT on 16 October 2001. (Revised 29 March 2004.) Paper accepted 29 April 2004. Paper published 20 May 2004.

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

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