Topology of hypersurface singularities with 3-dimensional critical set

TL;DR

This paper proves that the Milnor fiber of certain 3-dimensional hypersurface singularities has a homotopy type equivalent to a bouquet of spheres, under specific codimension conditions.

Contribution

It establishes a new topological characterization of Milnor fibers for hypersurface singularities over 3-dimensional i.c.i.s. with finite extended codimension.

Findings

Milnor fiber homotopy type is a bouquet of spheres

Applicable to singularities over 3-dimensional i.c.i.s.

Conditions involve finite extended codimension

Abstract

In this paper, we prove that the Milnor fibre of a singularity over an i.c.i.s. of dimension 3 has the homotopy type of a bouquet of spheres, provided that the function that defines the singularity has finite extended codimension with respect to the ideal that defines the i.c.i.s.