Surface links and their generic planar projections

Osamu Saeki, Yasushi Takeda

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We often study surface links in 4-space by using their projections into 3-space, or their broken surface diagrams. It is well-known that a broken surface diagram recovers the given surface link. In this paper, we study surface links in 4-space by using their generic projections into the plane. These projections have fold points and cusps as their singularities in general. We consider the question whether such a generic planar projection can recover the given surface link. We introduce the notion of banded braids, and show that a generic planar projection together with banded braids associated to the segments of the fold curve image can recover the given surface link. As an application, we give a new proof to the Whitney congruence concerning the normal Euler number of surface links.

Original languageEnglish
Pages (from-to)41-66
Number of pages26
JournalJournal of Knot Theory and its Ramifications
Volume18
Issue number1
DOIs
Publication statusPublished - Jan 2009

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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