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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Abstract
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 |
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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 |
URI: | http://srodev.sussex.ac.uk/id/eprint/78295 |
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