Geodesic
Unlinking singular loci from regular fibers and its application to submersions
Journal of Singularities, Tome 22 (2020), pp. 92-103

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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.
DOI : 10.5427/jsing.2020.22f
Classification : 57R45, 57R30, 58K30, 57M25, 57R20. 
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     author = {Osamu Saeki},
     title = {Unlinking singular loci from regular fibers and its application to submersions},
     journal = {Journal of Singularities},
     pages = {92--103},
     publisher = {mathdoc},
     volume = {22},
     year = {2020},
     doi = {10.5427/jsing.2020.22f},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22f/}
}
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Osamu Saeki. Unlinking singular loci from regular fibers and its application to submersions. Journal of Singularities, Tome 22 (2020), pp. 92-103. doi: 10.5427/jsing.2020.22f

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