Link theory and new restrictions for \(M\)-curves of degree nine. (English. Russian original) Zbl 0972.14041

Orevkov, S. Yu.

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.

Reviewer: Eugenii I.Shustin (Tel Aviv)

MSC:

14P25	Topology of real algebraic varieties
57M25	Knots and links in the \(3\)-sphere (MSC2010)
20F36	Braid groups; Artin groups

Keywords:

real plane algebraic curve; quasipositive braids; Murasugi-Tristram inequality

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