Abstract
A divide is the image of a generic, relative immersion of intervals in the unit disk. In the present paper we remove the relative condition by introducing a generalized class of divide called free divides . We describe how to define the link of a free divide in a well-defined way and, further, show that its unknotting (gordian) number is still equal to the number of double points of the immersed intervals. This extends the result of A'Campo concerning unknotting numbers of just relative divides. We conclude the paper with a table of free divides and their links which, by virtue of the main result, are tabulated according to their unknotting numbers.
| Original language | English |
|---|---|
| Pages (from-to) | 609-636 |
| Number of pages | 28 |
| Journal | Topology and its Applications |
| Volume | 123 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2002 Sept 30 |
| Externally published | Yes |
Keywords
- 4-genus
- Divide
- Knot theory
- Slice Euler characteristic
- Unknotting number
ASJC Scopus subject areas
- Geometry and Topology