# The boundary of the Milnor fibre of certain non-isolated singularities

## TL;DR

This paper determines the topology of the boundary of the Milnor fibre for certain non-isolated singularities by analyzing the double-point-geometry of a finitely determined complex germ.

## Contribution

It introduces a method to compute the plumbing graph of the Milnor fibre boundary from the double-point-geometry of the germ.

## Key findings

- Provides explicit plumbing graphs for specific non-isolated singularities
- Links the topology of Milnor fibre boundaries to the germ's double-point-geometry
- Advances understanding of non-isolated hypersurface singularities

## Abstract

Let $ \Phi: ({\mathbb C}^2, 0) \to ( {\mathbb C}^3, 0) $ be a finitely determined complex analytic germ and let $(\{f=0\},0)$ be the reduced equation of its image, a non-isolated hypersurface singularity. We provide the plumbing graph of the boundary of the Milnor fibre of $f$ from the double-point-geometry of $\Phi$.