Abstract
We prove two structure theorems for the Gromov-Witten theory of the quintic threefolds, which together give an effective algorithm for the all genus Gromov-Witten potential functions of quintics. By using these structure theorems, we prove Yamaguchi-Yau's Polynomial Ring Conjecture in this paper and prove Bershadsky-Cecotti-Ooguri-Vafa's Feynman rule conjecture in the subsequent paper.
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