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- W4246820565 abstract "If a closed curve in an orientable surface bounds a disk in a handlebody, then the double points on the boundary admit certain pairings that are called filamentations. Intersection numbers are associated to the filamentations; these numbers provide a necessary criterion for the existence of a disk bounded by a given curve. As an application, a closed curve with three generic double points in a surface of genus 2 is given that bounds no disk in a handlebody. This is the most simple example of a closed curve that does not bound a disk. The example is generalized to find for each $n > 3$, a closed curve with $n$ crossings that does not bound a disk." @default.
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- W4246820565 date "1991-11-01" @default.
- W4246820565 modified "2023-09-26" @default.
- W4246820565 title "Closed Curves That Never Extend to Proper Maps of Disks" @default.
- W4246820565 doi "https://doi.org/10.2307/2048628" @default.
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