Milnor-Hamm sphere fibrations and the equivalence problem

TL;DR

This paper introduces a new sphere fibration concept for real map germs with radial discriminant, compares it to the Milnor-Hamm tube fibration, and establishes conditions for their equivalence and related open book structures.

Contribution

It proposes a novel sphere fibration framework for real map germs and provides criteria for its equivalence with the Milnor-Hamm fibration, including the existence of open book structures.

Findings

Established conditions for the equivalence of sphere and Milnor-Hamm fibrations.

Proved the existence of open book structures with singularities under natural conditions.

Provided a solution to the equivalence problem for these fibrations.

Abstract

We introduce the sphere fibration for real map germs with radial discriminant and we address the problem of its equivalence with the Milnor-Hamm tube fibration. Under natural conditions, we prove the existence of open book structures with singularities and solve the equivalence problem.