Chart descriptions of regular braided surfaces (Q2405074)

The paper under review is in the PL category. The authors investigate braided surfaces, continuing work of the first author. A surface braid is a properly embedded surface \(F\) in \(D_1^2 \times D_2^2\) such that the second projection \(\pi : D_1^2 \times D_2^2 \to D_2^2\) restricted to \(F\) is a branched covering map of \(F\), and \(\partial F \subset \partial (D_1^2 \times D_2^2)\) is the standard unlink (\(n\) points \(\times S^1\)). The previously introduced graphical method called ``chart description'' was useful in describing so called simple and embedded braided surfaces. This paper generalizes the chart description method to make it applicable to more general braided surfaces, so called regular braided surfaces (for each singular value there exists exactly one singular point). Then any regular braided surface is described by a regular chart description. Conversely, if a braided surface is described by a regular chart, then it is a regular braided surface. All simple braided surfaces are regular.