We study relative Gromov-Witten theory via universal relations provided by
the interaction of degeneration and localization. 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.Comment: 43 pages, revised & new surface calculation adde