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Doodles on surfaces
journal contribution
posted on 2023-06-09, 14:47 authored by Andrew Bartholomew, Roger Fenn, Naoko Kamada, Seiichi KamadaDoodles 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Journal of Knot Theory and Its RamificationsISSN
0218-2165Publisher
World Scientific PublishingExternal DOI
Issue
12Volume
27Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-08-28First Open Access (FOA) Date
2019-10-23First Compliant Deposit (FCD) Date
2018-08-24Usage metrics
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