Homotopy Type of Disentanglements of Multi-germs

TL;DR

This paper investigates the topological structure of disentanglements in complex analytic maps with isolated singularities, extending known results from mono-germs to a broad class of multi-germs.

Contribution

It provides a condition under which the disentanglement of multi-germs is a wedge of spheres, generalizing previous results for mono-germs.

Findings

Disentanglements are wedges of spheres under certain conditions.

The paper extends the understanding of topological structures in complex analytic maps.

Conditions for the sphere wedge decomposition are established for multi-germs.

Abstract

For a complex analytic map f from n-space to p-space with n<p and with an isolated instability at the origin, the disentanglement of f is a local stabilization of f that is analogous to the Milnor fibre for functions. For mono-germs it is known that the disentanglement is a wedge of spheres of possibly varying dimensions. In this paper we give a condition that allows us to deduce that the same is true for a large class of multi-germs.