zbMATH — the first resource for mathematics

Link theory and new restrictions for \(M\)-curves of degree nine. (English. Russian original) Zbl 0972.14041
Funct. Anal. Appl. 34, No. 3, 229-231 (2000); translation from Funkts. Anal. Prilozh. 34, No. 3, 84-87 (2000).
The author shows that certain arrangements of circles in the real projective plane cannot be isotopic to any real nonsingular algebraic curve of degree 9. This restriction is obtained by means of a new method developed by the author [S. Yu. Orevkov, Topology 38, 779-810 (1999; Zbl 0923.14032)] and based on the study of braids which can be associated with real plane algebraic curves. This is especially interesting, since other known methods apply mainly to curves of even degree. Proofs are sketchy, long computations are omitted.

14P25 Topology of real algebraic varieties
57M25 Knots and links in the \(3\)-sphere (MSC2010)
20F36 Braid groups; Artin groups
Full Text: DOI
[1] V. A. Rokhlin, Usp. Mat. Nauk,33, No. 5, 77–89 (1978).
[2] T. Fiedler, Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 6, 853–863 (1982).
[3] O. Ya. Viro, Izv. Akad. Nauk SSSR, Ser. Mat.,47, No. 5, 1135–1150 (1983).
[4] A. B. Korchagin, In: Lect. Notes in Math., vol. 1524, 1991, pp. 407–426.
[5] S. Yu. Orevkov, Topology,38, No. 4, 779–810 (1999); Erratum, ibid. (to appear). · Zbl 0923.14032 · doi:10.1016/S0040-9383(98)00021-4
[6] O. Ya. Viro and V. I. Zvonilov, Algebra Analiz,4, 539–548 (1993).
[7] O. Ya. Viro, Usp. Mat. Nauk,41, No. 3, 43–67 (1986).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.