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Topology of a polynomial of two complex variables at the neighbourhood of infinity. (Topologie d’un polynôme de deux variables complexes au voisinage de l’infini.) (French) Zbl 0855.32018
Summary: We give a complete system of invariants for the topological conjugacy of polynomials of \(\mathbb{C}^2\) outside a big enough compact set in the two possible versions: as foliations (forgetting the values of the fibers) and as functions. These invariants are described as a weighted and colored tree, that is obtained after reduction of singularities of the polynomial in the line of infinity. We give regularity criterion for the values of a polynomial and a description of the topology of its fibers used in the construction of the topological conjugacy from the tree.

MSC:
32S45 Modifications; resolution of singularities (complex-analytic aspects)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14B05 Singularities in algebraic geometry
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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