TY - JOUR
T1 - Unlinking singular loci from regular fibers and its application to submersions
AU - Saeki, Osamu
N1 - Funding Information:
The author would like to express his sincere gratitude to Professor David Chillingworth for stimulating discussions and for indicating the works of Hector and Peralta-Salas [9, 15]. He would also like to thank the anonymous referee for invaluable comments that improved the presentation of the paper. The author has been supported in part by JSPS KAKENHI Grant Numbers JP16K13754, JP16H03936, JP17H06128.
Publisher Copyright:
© 2020, Worldwide Center of Mathematics. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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U2 - 10.5427/jsing.2020.22f
DO - 10.5427/jsing.2020.22f
M3 - Article
AN - SCOPUS:85094165991
SN - 1949-2006
VL - 22
SP - 92
EP - 103
JO - Journal of Singularities
JF - Journal of Singularities
ER -