## Homotopy classification of nondegenerate quasiperiodic curves on the 2-sphere.(English)Zbl 1274.53055

Summary: We classify the curves on $$S^2$$ with fixed monodromy operator and nowhere vanishing geodesic curvature. The number of connected components of the space of such curves turns out to be 2 or 3 depending on the corresponding monodromy. This allows us to classify completely symplectic leaves of the Zamolodchikov algebra, the next case after the Virasoro algebra in the natural hierarchy of the Poisson structures on the spaces of linear differential equations.

### MSC:

 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 55R65 Generalizations of fiber spaces and bundles in algebraic topology