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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory