Carrousel in family and non-isolated hypersurface singularities in $C^3$

Abstract

We study the boundary $L_t$ of the Milnor fiber for the reduced holomorphic germs $f:({\mathbb{C}}^3,0)\to (\mathbb{C},0)$ having a non-isolated singularity at $0$. We prove that $L_t$ is a graph manifold by using a new technique of carrousel depending on one parameter varying on a circle. Our results enable one to compare the topology of $L_t$ and of the link of the normalization of $f^{-1}(0)$.

arXiv comment40 pages. Figures added. To appear in Journal für die reine und angewandte Mathematik (Crelle's Journal)