Holomorphic curves in Exploded Torus Fibrations: Compactness

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dc.creatorParker, Brett
dc.date2007-06-26
dc.date2008-01-14
dc.date.accessioned2026-07-07T08:53:58Z
dc.date.available2026-07-07T08:53:58Z
dc.descriptionThe category of exploded torus fibrations is an extension of the category of smooth manifolds in which some adiabatic limits look smooth. (For example, the limits considered in tropical geometry appear smooth, also degenerations corresponding to an algebraic family with normal crossing singularities are smooth.) In this paper we prove a compactness theorem for (pseudo)-holomorphic curves in exploded torus fibrations. In the case of smooth manifolds, this is just a version of Gromov's compactness theorem in a topology strong enough for gluing analysis.
dc.description68 pages, 21 figures, v2: error in definition of `basic' corrected, improved exposition
dc.identifierhttps://arxiv.org/abs/0706.3917
dc.identifierhttp://arxiv.org/abs/0706.3917
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145765
dc.subjectSymplectic Geometry
dc.subjectAnalysis of PDEs
dc.subject57R17
dc.titleHolomorphic curves in Exploded Torus Fibrations: Compactness
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