Singular open book structures from real mappings

TL;DR

This paper extends Milnor's theorem to nonisolated singularities in real mappings, identifying new classes of real analytic mappings with singularities that still admit Milnor fibrations and open book structures.

Contribution

It introduces generalized Milnor fibrations for germs with nonisolated singularities, expanding the understanding of open book structures in real analytic mappings.

Findings

Established Milnor fibrations for new classes of real mappings with nonisolated singularities.

Proved extensions of Milnor's theorem applicable to germs with positive dimensional singular loci.

Identified conditions under which real analytic mappings admit open book structures with singular binding.

Abstract

We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus $\Sing \psi \subset \psi^{-1}(0)$, for which the Milnor fibration exists and yields an open book structure with singular binding.