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We state a version of the crepant resolution conjecture for total ancestorpotentials for surface singularities, and reduce the conjecture to the quantumMcKay correspondence conjecture of J.Bryan and A.Gholampour and a vanishingconjecture for Hurwitz-Hodge integrals. In particular, for singularities oftype A, we prove the conjecture. We also suggest an approach towards a prooffor the general cases by Teleman's reconstruction theorem for semisimplecohomological field theories.

On the Crepant Resolution Conjecture for Gromov-Witten Gravitational Ancestors in All Genera for Surface Singularities