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

Tsuyoshi Kobayashi, Osamu Saeki

Research output: Contribution to journalArticlepeer-review

24 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
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map'. Together they form a unique fingerprint.

Cite this