A topological view of Gromov–Witten theory

We study relative Gromov–Witten theory via universal relations provided by the degeneration and localization formulas. We find relative Gromov–Witten theory is completely determined by absolute Gromov–Witten theory. The relationship between the relative and absolute theories is guided by a strong analogy to classical topology.As an outcome, we present a mathematical determination of the Gromov–Witten invariants (in all genera) of the Calabi–Yau quintic 3-fold in terms of known theories.