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The aim of Part II is to explore the technique of invariance of tautological equations in the realm of Gromov--Witten theory. The main result is a proof of Invariance Theorem (Invariance Conjecture~1 in [14]), via the techniques from Gromov--Witten theory. It establishes some general inductive structure of the tautological rings, and provides a new tool to the study of this area.

This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.

A new tautological equation of $\bar{M}_{3,1}$ in codimension 3 is derived and proved, using the invariance condition explained in earlier works.

The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of V×W with those of V and W in the case the log structure on V is trivial.