Plane real algerbaic curves of odd degree with a deep nest

2003/11/26 by S. Yu. Orevkov, Stepan Yu Orevkov, Orevkov, Stepan Yu
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algorithm #Computation #Degree (music) #FOS: Mathematics #Generalization #Geometric Topology (math.GT) #Geometry #Iterated function #Mathematical analysis #Mathematics #Physics #Pure mathematics #Torus #math.GT

paper · pdf · doi:10.48550/arxiv.math/0311478

5 pages. Only the title has changed

openalex publication_date 2003/11/26 · arxiv created 2004/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We apply Murasugi-Tristram inequality to real algebraic curves of odd degree on RP² with a deep nest, i.e. a nest of the depth k-1 where 2k+1 is the degree. For such curves, the ingredients of the Murasugi-Tristram inequality can be computed (or estimated) inductively using the computations for iterated torus links due to Eisenbud and Neumann as the base of the induction and Conway's skein relation as the induction step. In Appendix B, we give some generalization of the skein relation.

Citations

• LINK THEORY AND OVAL ARRANGEMENTS OF REAL ALGEBRAIC CURVES

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