Deformations with fibre constancy

TL;DR

This paper investigates conditions that ensure deformations of maps preserve the general fibers while simplifying singularities, aiding the study of local topology.

Contribution

It provides specific conditions under which deformations maintain fiber constancy during singularity simplification.

Findings

Identifies criteria for fiber-preserving deformations

Establishes theoretical conditions for local topology analysis

Enhances understanding of singularity splitting

Abstract

For studying the local topology of maps, one uses deformations which split the singularities into simpler ones while preserving the general fibres. We give conditions under which such conservation holds.