THE TOPOLOGICAL VERTEX
This chapter explains the cut-and-paste approach to toric Calabi-Yau manifolds developed previously with the large-N duality relating Chern-Simons theory and topological strings, to find a building block for topological string amplitudes on those geometries. This building block is an open string amplitude called the topological vertex. In order to understand topological vertex it is necessary to discuss one aspect of open string amplitudes: the framing ambiguity. Three gluing rules for the topological vertex are discussed: for a change of orientation in one edge, for the propagator, and for the matching of framings in the gluing. Some examples of computation of topological string amplitudes by using the topological vertex are presented.
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