Lips and swallow-tails of singularities of product maps

Kazuto Takao

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.

DOI: 10.5427/jsing.2014.10t

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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:


Author(s) information:

Kazuto Takao
Institute of Mathematics for Industry
Kyushu University
744 Motooka
Nishi-ku Fukuoka 819-0395, Japan