In this paper we show that the polynomial structure of the topological string partition function found by Yamaguchi and Yau for the quintic holds for an arbitrary Calabi-Yau manifold with any number of moduli. Furthermore, we generalize these results to the open topological string partition function as discussed recently by Walcher and reproduce his results for the real quintic.

We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror symmetry at any point in the moduli space. Holomorphic ambiguities of the anomaly equations are fixed by global information obtained from boundary conditions at few special divisors in the moduli space. As an illustration we compute higher genus orbifold Gromov-Witten invariants for

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For a given attractor black hole with generic D6-D4-D2-D0-charges in four dimensions we identify the set of supersymmetric branes, static or stationary in global coordinates, of the corresponding eleven-dimensional near horizon geometry. The set of these BPS states, which includes branes which partially or fully wrap the horizon, should play a role in understanding the partition function of black holes with D6-charges.