# Links and gordian numbers associated with generic immersions of intervals

William Gibson, Masaharu Ishikawa

10 引用 (Scopus)

### 抄録

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.

元の言語 English 609-636 28 Topology and its Applications 123 3 https://doi.org/10.1016/S0166-8641(01)00224-3 Published - 2002 9 30 Yes

### Fingerprint

Immersion
Divides
Unknotting number
Interval
Unit Disk
Well-defined
Table

### ASJC Scopus subject areas

• Geometry and Topology

### これを引用

：: Topology and its Applications, 巻 123, 番号 3, 30.09.2002, p. 609-636.

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