Unlinking singular loci from regular fibers and its application to submersions

Osamu Saeki

Journal of Singularities
volume 22 (2020), 92-103

Received: 28 February 2019. Received in revised form: 4 August 2019.

DOI: 10.5427/jsing.2020.22f

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Abstract:

Given a null-cobordant oriented framed link L in a closed oriented 3-manifold M, we study the condition for the existence of a generic smooth map of M to the plane that has L as an oriented framed regular fiber such that the singular point set is unlinked with L. As an application, we give a singularity theoretical proof to the theorem, originally proved by Hector, Peralta-Salas and Miyoshi, about the realization of a link in an open oriented 3-manifold as a regular fiber of a submersion to the plane.

2000 Mathematical Subject Classification:

Primary 57R45; Secondary 57R30, 58K30, 57M25, 57R20.

Key words and phrases:

Submersion, link, 3-manifold, excellent map, singular point set, regular fiber, relative Stiefel-Whitney class, framing

Author(s) information:

Osamu Saeki
Institute of Mathematics for Industry
Kyushu University
Motooka 744
Nishi-ku, Fukuoka 819-0395, Japan
email: saeki@imi.kyushu-u.ac.jp