Open Access
2008 Growth of Casson handles and transversality for ASD moduli spaces
Tsuyoshi Kato
Geom. Topol. 12(3): 1265-1311 (2008). DOI: 10.2140/gt.2008.12.1265


In this paper we study the growth of Casson handles which appear inside smooth four-manifolds. A simply-connected and smooth four-manifold admits decompositions of its intersection form. Casson handles appear around one side of the end of them, when the type is even. They are parameterized by signed infinite trees and their growth measures some of the complexity of the smooth structure near the end. We show that with respect to some decompositions of the forms on the K3 surface, the corresponding Casson handles cannot be of bounded type in our sense. In particular they cannot be periodic. The same holds for all logarithmic transforms which are homotopically equivalent to the K3 surface. We construct Yang–Mills gauge theory over Casson handles of bounded type, and verify that transversality works over them.


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Tsuyoshi Kato. "Growth of Casson handles and transversality for ASD moduli spaces." Geom. Topol. 12 (3) 1265 - 1311, 2008.


Received: 12 May 2006; Revised: 22 April 2008; Accepted: 5 October 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1148.57022
MathSciNet: MR2421128
Digital Object Identifier: 10.2140/gt.2008.12.1265

Primary: 57M30 , 57R57
Secondary: 14J80

Keywords: Casson handles , transversality , Yang-Mills theory

Rights: Copyright © 2008 Mathematical Sciences Publishers

Vol.12 • No. 3 • 2008
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