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Title: Seiberg-Witten Theory and the Topology of Elliptic surfaces
Authors: Segert, Simon
Advisors: Szabo, Zoltan
Contributors: Nemethi, Andras
Department: Mathematics
Class Year: 2014
Abstract: The Seiberg-Witten invariant provides dramatic information about smooth manifolds-in particular it allows for the possibility of distinguishing different smooth structures on the same topological manifold. In this paper, we will outline the construction of infinitely many distinct smooth structures on one particularly simple 4-manifold: the K3 surface, and show how to use the Seiberg-Witten invariant to distinguish them. To do this, we will need two essentially different sets of tools: gauge theory on the one hand, and Kirby calculus and general techniques of 4-manifold topology on the other. We will develop both sets of techniques, and then show how, using the rational blowdown procedure discovered by Fintushel and Stern in [5], they may be combined to produce striking results. All the material covered is standard, and may be found in many references, such as [2], [8] or [17].
Extent: 52 pages
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2020

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