Instantons on cylindrical manifolds and stable bundles. (English) Zbl 1069.53029

This is a modified version of the PhD thesis prepared by the author at the Columbia University. He proves the theorem conjectured by S. K. Donaldson [N. J. Hitchin (ed.), Lond. Math. Soc. Lect. Note Ser. 208, 119–138 (1995; Zbl 0829.57011)] which states that for a given smooth complex curve \(\Sigma\) the space \({\mathcal M}/{\mathcal I}\), where \({\mathcal M}\), is the moduli space of finite energy \(U(2)\)-instantons over \(\Sigma\times S^1\times \mathbb R\) is naturally homeomorphic to \(\mathcal Z\), where \(\mathcal Z\) is the space of isomorphism classes of rank 2 holomorphic bundles over \(S=\Sigma\times\mathbb{C} P^1\).


53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
57R58 Floer homology
14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)


Zbl 0829.57011
Full Text: DOI arXiv EuDML EMIS


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