Doodles on surfaces

Bartholomew, Andrew, Fenn, Roger, Kamada, Naoko and Kamada, Seiichi (2018) Doodles on surfaces. Journal of Knot Theory and Its Ramifications, 27 (12). ISSN 0218-2165

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Doodles were introduced in but were restricted to embedded circles in the 2-sphere. Khovanov, extended the idea to immersed circles in the 2-sphere. In this paper we further extend the range of doodles to any closed oriented surfaces. Uniqueness of minimal representatives is proved, and various example of doodles are given with their minimal representatives. We also introduce the notion of virtual doodles, and show that there is a natural one-to-one correspondence between doodles on surfaces and virtual doodles on the plane.

Item Type: Article
Keywords: doodles, virtual doodles, minimal diagrams, immersed circles
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Jodie Bacon
Date Deposited: 28 Aug 2018 08:49
Last Modified: 06 Dec 2018 17:23

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