Holomorphic curves in Exploded Torus Fibrations: Compactness

Details Holomorphic curves in Exploded Torus Fibrations: Compactness Holomorphic curves in Exploded Torus Fibrations: Compactness

2007-06-26

arxiv.org/abs/0706.3917v2

Mathematics

Symplectic Geometry

68 pages, 21 figures, v2: error in definition of `basic' corrected, improved exposition

Scientific paper

The 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.

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