Linking between singular locus and regular fibers

Osamu Saeki

Journal of Singularities
volume 21 (2020), 234-248

Received: 31 March 2018. Received in revised form: 20 September 2018.

DOI: 10.5427/jsing.2020.21n

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Abstract:

Given a null-cobordant oriented framed link L in a closed oriented 3-manifold M, we determine those links in M - L which can be realized as the singular point set of a generic map M -> R^2 that has L as an oriented framed regular fiber. Then, we study the linking behavior between the singular point set and regular fibers for generic maps of M into R^2.

2000 Mathematical Subject Classification:

Primary: 57R45; Secondary: 58K30, 57M25, 57R20, 57R70

Key words and phrases:

Excellent map, 3-manifold, 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