Fibrations of highly singular map germs

TL;DR

This paper introduces new local fibration structures for real map germs with highly singular discriminants, expanding the understanding of their topological behavior.

Contribution

It defines local and complete local fibration structures for real map germs with positive-dimensional discriminants and provides new classes of such germs with these structures.

Findings

Established local fibration structures over the complement of the discriminant.

Developed complete local fibration structures including the stratified discriminant.

Identified new classes of map germs with these fibration structures.

Abstract

We define local fibration structures for real map germs with strictly positive dimensional discriminant: a local fibration structure over the complement of the discriminant, and a complete local fibration structure which includes the stratified discriminant into the picture. We provide new classes of map germs endowed with such local fibration structures.