Heegaard splittings and singularities of the product map of Morse functions
arXiv:1205.1206 · doi:10.1090/S0002-9947-2013-06015-1
Abstract
We give an upper bound for the Reidemeister-Singer distance between two Heegaard splittings in terms of the genera and the number of cusp points of the product map of Morse functions for the splittings. It suggests that a certain development in singularity theory may lead to the best possible bound for the Reidemeister-Singer distance.
18 pages, 10 figures, v3: minor corrections throughout the paper