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

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].

### 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

Zbl 0853.32003
Full Text: