PU(2) monopoles. III: Existence of gluing and obstruction maps

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dc.creatorFeehan, Paul M. N.
dc.creatorLeness, Thomas G.
dc.date1999-07-16
dc.date1999-07-20
dc.date.accessioned2026-07-07T05:29:56Z
dc.date.available2026-07-07T05:29:56Z
dc.descriptionThis is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. The moduli space of solutions to the PU(2) monopole equations provides a noncompact cobordism between links of compact moduli spaces of U(1) monopoles of Seiberg-Witten type and the moduli space of anti-self-dual SO(3) connections, which appear as singularities in this larger moduli space. In this paper we prove the first part of a general gluing theorem for PU(2) monopoles, with the proof of the second half to appear in a companion article. The ultimate purpose of the gluing theorem is to provide topological models for neighborhoods of ideal Seiberg-Witten moduli spaces appearing in lower levels of the Uhlenbeck compactification of the moduli space of PU(2) monopoles and thus permit calculations of their contributions to Donaldson invariants using the PU(2)-monopole cobordism.
dc.descriptionLaTeX 2e, 92 pages. Minor typos corrected
dc.identifierhttps://arxiv.org/abs/math/9907107
dc.identifierhttp://arxiv.org/abs/math/9907107
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78835
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectAnalysis of PDEs
dc.titlePU(2) monopoles. III: Existence of gluing and obstruction maps
dc.typetext

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