Absolute vs. Relative Gromov-Witten Invariants
Algebraic Geometry
2014-05-13 v2 Symplectic Geometry
Abstract
In light of recent attempts to extend the Cieliebak-Mohnke approach for constructing Gromov-Witten invariants to positive genera, we compare the absolute and relative Gromov-Witten invariants of compact symplectic manifolds when the symplectic hypersurface contains no relevant holomorphic curves. We show that these invariants are then the same, except in a narrow range of dimensions of the target and genera of the domains, and provide examples when they fail to be the same.
Cite
@article{arxiv.1405.2045,
title = {Absolute vs. Relative Gromov-Witten Invariants},
author = {Mohammad F. Tehrani and Aleksey Zinger},
journal= {arXiv preprint arXiv:1405.2045},
year = {2014}
}
Comments
46 pages, 11 figures, 4 tables; added Rmk 3.1 and modified Rmk 5.4 after initial feedback