Mathematics – Algebraic Geometry
Scientific paper
1996-08-12
Mathematics
Algebraic Geometry
LaTeX2e with AMS-fonts, 73 pages, 3 figures, full revision 12/1997
Scientific paper
We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping spaces from (prestable) algebraic curves into the symplectic manifold with the structure of a Banach orbifold and then exhibiting the space of stable $J$-curves (``stable maps'') as zero set of a Fredholm section of a Banach orbibundle over this space. The invariants are constructed by pairing with a homology class on the locally compact topological space of stable $J$-curves that is generated as localized Euler class of the section.
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