On Bennequin’s problem: a counterexample (after Alexander). (Sur le problème de Bennequin: un contre-exemple (d’après Alexander).) (French) Zbl 0895.53042

Dufresnoy, Alain

Séminaire de théorie spectrale et géométrie. Année 1996-1997. St. Martin D’Hères: Univ. de Grenoble I, Institut Fourier, Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 15, 13-15 (1997).

An analytic disk in \(\mathbb C^n\) is a map \(f:\overline D\to\mathbb C^n\) where \(\overline D\) is the closed unit disk, holomorphic on the open disk \(D\) and smooth up to boundary. The aim of this paper is to present a counterexample obtained by H. Alexander to a problem of D. Bennequin asserting that a non-constant analytic disk exists in \(\mathbb C^2\) with boundary in a totally real 2-torus. There is also presented a true weak version of Bennequin’s problem obtained by H. Alexander [Invent. Math. 125, 135-148 (1996; Zbl 0853.32003)].
For the entire collection see [Zbl 0882.00016].

Reviewer: M.Crasmareanu (Iaşi)

MSC:

53C23	Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
32A10	Holomorphic functions of several complex variables

Keywords:

analytic disk; totally real torus; Gromov’s method

Citations:

Zbl 0853.32003