Real Milnor Fibres and Puiseux Series

Goulwen Fichou (1) , Masahiro Shiota (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Graduate School of Mathematics [Nagoya]

Given a real polynomial function and a point in its zero locus, we defined a set consisting of algebraic real Puiseux series naturally attached to these data. We prove that this set determines the topology and the geometry of the real Milnor fibre of the function at this point. To achieve this goal, we balance between the tameness properties of this set of Puiseux series, considered as a real algebraic object over the field of algebraic Puiseux series, and its behaviour as an infinite dimensional object over the real numbers.

Mots clés: semialgebraic homology; Milnor fibres; PL-topology

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou, Masahiro Shiota. Real Milnor Fibres and Puiseux Series. Annales Scientifiques de l'École Normale Supérieure, 2017, 50 (5), pp.1205-1240. ⟨hal-00978433⟩