Real algebraic overtwisted contact structures on 3-spheres

Karadereli, Şeyma¹ ; Öztürk, Ferit¹

¹Department of Mathematics, Boğaziçi University, Istanbul, Turkey

Algebraic and Geometric Topology, Tome 25 (2025) no. 3, pp. 1377-1409

Résumé

A real algebraic link in the 3-sphere is defined as the zero locus in the 3-sphere of a real algebraic function from ℝ4 to ℝ2 with an isolated singularity at the origin. A real algebraic open book decomposition on the 3-sphere is by definition the Milnor fibration of such a real algebraic function. We prove that every overtwisted contact structure on the 3-sphere with positive three-dimensional invariant d3 (apart from 13 exceptions) are real algebraic via functions of the form fḡ with f,g complex algebraic and with the pages of the associated open books planar.

Détail

DOI : 10.2140/agt.2025.25.1377

Keywords: real algebraic link, overtwisted contact structure

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