Skew-symmetric augmented matrices and a characterization of virtual doodles
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917879673257984 |
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| author | Ocampo, Oscar Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia |
| author_facet | Ocampo, Oscar Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skew-symmetric augmented matrices and a characterization of virtual doodles Ocampo, Oscar Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Geometric Topology 57K12 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. |
| title | Skew-symmetric augmented matrices and a characterization of virtual doodles |
| topic | Geometric Topology 57K12 |
| url | https://arxiv.org/abs/2412.18959 |