Unlinking singular loci from regular fibers and its application to submersions

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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.

Original languageEnglish
Pages (from-to)92-103
Number of pages12
JournalJournal of Singularities
Volume22
DOIs
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Applied Mathematics

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