Separation by a codimension-1 map with a normal crossing point

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Abstract

Let f:Mn-1→Nn be an immersion with normal crossings of a closed orientable (n-1)-manifold into an orientable n-manifold. We show, under a certain homological condition, that if f has a multiple point of multiplicity m, then the number of connected components of N-f(M) is greater than or equal to m+1, generalizing results of Biasi and Romero Fuster (Illinois J. Math.36 (1992), 500-504) and Biasi, Motta and Saeki (Topology Appl.52 (1993), 81-87). In fact, this result holds more generally for every codimension-1 continuous map with a normal crossing point of multiplicity m. We also give various geometrical applications of this theorem, among which is an application to the topology of generic space curves.

Original languageEnglish
Pages (from-to)235-247
Number of pages13
JournalGeometriae Dedicata
Volume57
Issue number3
DOIs
Publication statusPublished - Oct 1 1995
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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