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- Title
SURFACE LINKS AND THEIR GENERIC PLANAR PROJECTIONS.
- Authors
SAEKI, OSAMU; TAKEDA, YASUSHI
- 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.
- Subjects
GRAPHIC methods; PLANE geometry; PLANE curves; EULER characteristic; GEOMETRIC congruences
- Publication
Journal of Knot Theory & Its Ramifications, 2009, Vol 18, Issue 1, p41
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216509006847