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15 February 2005 Curves in Calabi-Yau threefolds and topological quantum field theory
Jim Bryan, Rahul Pandharipande
Duke Math. J. 126(2): 369-396 (15 February 2005). DOI: 10.1215/S0012-7094-04-12626-0

Abstract

We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau threefolds.

We define relative invariants for local theory which give rise to a (1+1)-dimensional topological quantum field theory (TQFT) taking values in the ring $\mathbb{Q}[[t]]$. The associated Frobenius algebra over $\mathbb{Q}[[t]]$ 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 the case where either the target genus or the degree equals 1.

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Jim Bryan. Rahul Pandharipande. "Curves in Calabi-Yau threefolds and topological quantum field theory." Duke Math. J. 126 (2) 369 - 396, 15 February 2005. https://doi.org/10.1215/S0012-7094-04-12626-0

Information

Published: 15 February 2005
First available in Project Euclid: 21 January 2005

zbMATH: 1084.14053
MathSciNet: MR2115262
Digital Object Identifier: 10.1215/S0012-7094-04-12626-0

Subjects:
Primary: 14N35

Rights: Copyright © 2005 Duke University Press

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Vol.126 • No. 2 • 15 February 2005
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