The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map

Tsuyoshi Kobayashi, Osamu Saeki

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We show that Rubinstein-Scharlemann graphics for 3-manifolds can be regarded as the images of the singular sets (: discriminant set) of stable maps from the 3-manifolds into the plane. As applications of our understanding of the graphic, we give a method for describing Heegaard surfaces in 3-manifolds by using arcs in the plane, and give an orbifold version of Rubinstein-Scharlemann's setting. Then by using this setting, we show that every genus one 1-bridge position of a nontrivial two bridge knot is obtained from a 2-bridge position in a standard manner.

Original languageEnglish
Pages (from-to)101-156
Number of pages56
JournalPacific Journal of Mathematics
Volume195
Issue number1
DOIs
Publication statusPublished - Sep 2000

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Stable Map
Discriminant
Singular Set
Orbifold
Knot
Genus
Arc of a curve
Graphics

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map. / Kobayashi, Tsuyoshi; Saeki, Osamu.

In: Pacific Journal of Mathematics, Vol. 195, No. 1, 09.2000, p. 101-156.

Research output: Contribution to journalArticle

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