|GÖKOVA GEOMETRY / TOPOLOGY PROCEEDINGS|
||Proceedings of Gökova Geometry-Topology Conference 2006|
Initiated by Gromov in , the study of holomorphic curves in symplectic manifolds has been a powerfull tool in symplectic topology, however the moduli space of holomorphic curves is often very difficult to find. A common technique is to study the limiting behavior of holomorphic curves in a degenerating family of complex structures which corresponds to a kind of adiabatic limit. The category of exploded fibrations is an extension of the smooth category in which some of these degenerations can be described as smooth families.
The first part of this paper is devoted to defining exploded fibrations and a slightly more specialized category of exploded
fibrations. In section 6 are some examples of holomorphic curves in exploded
fibrations, including a brief discussion of the relationship between tropical geometry and exploded
fibrations. In section 7, it is shown that exploded fibrations have a good intersection theory. In section 8, the perturbation theory of holomorphic curves in exploded
fibrations is sketched.
||holomorphic curves, symplectic topology, log structure, tropical geometry, exploded fibrations, adiabatic limit|
2006 Proceedings main page|
Last updated: January 2008
Wed address: GokovaGT.org/proceedings/2006