Virtual Strings for Closed Curves with Multiple Components
| dc.creator | Schellhorn, William J. | |
| dc.date | 2004-12-01 | |
| dc.date | 2005-03-08 | |
| dc.date.accessioned | 2026-07-07T05:14:52Z | |
| dc.date.available | 2026-07-07T05:14:52Z | |
| dc.description | A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve has an underlying virtual string and every virtual string has an underlying Gauss paragraph. A word-wise partition is a partition of the alphabet set of a Gauss paragraph that satisfies certain conditions with respect to the Gauss paragraph. In this paper we use the theory of virtual strings to obtain a combinatorial description of closed curves in the 2-sphere (and therefore 2-dimensional Euclidean space) in terms of Gauss paragraphs and word-wise partitions. | |
| dc.description | 35 pages, 5 figures. No fundamental changes were made between the second and third versions. The third version contains some clarifications in the definitions and proofs that will hopefully improve understanding | |
| dc.identifier | https://arxiv.org/abs/math/0412023 | |
| dc.identifier | http://arxiv.org/abs/math/0412023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73445 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99 | |
| dc.title | Virtual Strings for Closed Curves with Multiple Components | |
| dc.type | text |