ON THE DECOMPOSITION OF A 2D-COMPLEX GERM WITH NON-ISOLATED SINGULARITIES

Noémie Combe (1)

1 AMU - Aix Marseille Université

The decomposition of a two dimensional complex germ with non-isolated singular-ity into semi-algebraic sets is given. This decomposition consists of four classes: Riemannian cones defined over a Seifert fibered manifold, a topological cone over thickened tori endowed with Cheeger-Nagase metric, a topological cone over mapping torus endowed with Hsiang-Pati metric and a topological cone over the tubular neighbourhoods of the link's singularities. In this decomposition there exist semi-algebraic sets that are metrically conical over the manifolds constituting the link. The germ is reconstituted up to bi-Lipschitz equivalence to a model describing its geometric behavior.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Noémie Combe. ON THE DECOMPOSITION OF A 2D-COMPLEX GERM WITH NON-ISOLATED SINGULARITIES. 2015. ⟨hal-01128570⟩