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Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory

Jim Bryan·Rahul Pandharipande
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Abstract

We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau 3-folds. We define relative invariants for the local theory which give rise to a 1+1-dimensional TQFT taking values in the ring Q[[t]]. The associated Frobenius algebra over Q[[t]] is semisimple. Consequently, we obtain a structure result for the local invariants. As an easy consequence of our structure formula, we recover the closed formulas for the local invariants in case either the target genus or the degree equals 1.

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Jim Bryan, Rahul Pandharipande. 2004-05-11. Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory. https://arxiv.org/abs/math/0306316

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