Skew-symmetric augmented matrices and a characterization of virtual doodles

Autor:	Ocampo, Oscar, Rodríguez-Nieto, José Gregorio, Salazar-Díaz, Olga Patricia
Rok vydání:	2024
Předmět:	Mathematics - Geometric Topology 57K12
Druh dokumentu:	Working Paper
Popis:	In this paper, we present a brief overview of the concept of doodles from the perspective of J.S. Carter's work on classifying immersed curves and the work of J.S. Carter, S. Kamada, and M. Saito on stable equivalence of knots on surfaces and virtual knot cobordisms. We use the homology intersection number and the work of G. Cairns and D. Elton on the Gauss word problem to introduce the concept of skew-symmetric augmented matrices for determining whether a virtual doodle is non-classical. We also provide a characterization of the virtualization of classical doodles. Comment: 17 pages. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.18959 Zobrazit plný text záznamu View this record from Arxiv