Crossing numbers and rotation numbers of cycles in a plane immersed graph

Ayumu Inoue, Naoki Kimura, Ryo Nikkuni, Kouki Taniyama*

*この研究の対応する著者

研究成果: Article査読

抄録

For any generic immersion of a Petersen graph into a plane, the number of crossing points between two edges of distance one is odd. The sum of the crossing numbers of all 5-cycles is odd. The sum of the rotation numbers of all 5-cycles is even. We show analogous results for 6-cycles, 8-cycles and 9-cycles. For any Legendrian spatial embedding of a Petersen graph, there exists a 5-cycle that is not an unknot with maximal Thurston-Bennequin number, and the sum of all Thurston-Bennequin numbers of the cycles is seven times the sum of all Thurston-Bennequin numbers of the 5-cycles. We show analogous results for a Heawood graph. We also show some other results for some graphs. We characterize abstract graphs that have a generic immersion into a plane whose all cycles have rotation number 0.

本文言語English
論文番号2250076
ジャーナルJournal of Knot Theory and its Ramifications
31
11
DOI
出版ステータスPublished - 2022 10月 1

ASJC Scopus subject areas

  • 代数と数論

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