Journal of Singularities
volume 10 (2014), 286-295 January 04, 2013; Last modified version: July 23, 2013.
Received 4 January 2013. Received in revised form 23 July 2013.
Lips and swallow-tails are generic local moves of singularities of a smooth map to a 2-manifold. We prove that these moves of singularities of the product map of two functions on a 3-manifold can be realized by isotopies of the functions.
Morse function, stable map
Mathematical Subject Classification:
Institute of Mathematics for Industry
Nishi-ku Fukuoka 819-0395, Japan