## Curves in Calabi-Yau threefolds and Topological Quantum Field Theory (2008)

Citations: | 3 - 2 self |

### BibTeX

@MISC{Bryan08curvesin,

author = {Jim Bryan and Rahul P},

title = {Curves in Calabi-Yau threefolds and Topological Quantum Field Theory},

year = {2008}

}

### OpenURL

### Abstract

We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau threefolds. 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. 1 Notation, definitions and results A central problem in Gromov-Witten theory is to determine the structure of the Gromov-Witten invariants. Of special interest is the case where the target manifold is a Calabi-Yau threefold. We prove a structure result for the local Gromov-Witten invariants of a curve in a Calabi-Yau threefold. First, we define a relative version of the local invariants. In Theorem 1.2,