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We give an upper bound for the Reidemeister-Singer distance between twoHeegaard splittings in terms of the genera and the number of cusp points of theproduct map of Morse functions for the splittings. It suggests that a certaindevelopment in singularity theory may lead to the best possible bound for theReidemeister-Singer distance.

Heegaard splittings and singularities of the product map of Morse functions