The symplectic sum formula for Gromov–Witten invariants

Abstract

In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum $Z=X\# Y$ in terms of the relative GW invariants of $X$ and $Y$. Several applications to enumerative geometry are given.

Authors

Eleny-Nicoleta Ionel

Department of Mathematics
University of Wisconsin
Madison, WI 53706
United States

Thomas H. Parker

Department of Mathematics
Michigan State University
East Lansing, MI 48824
United States