Thom irregularity and Milnor tube fibrations

TL;DR

This paper identifies conditions under which real map germs admit Milnor tube fibrations, expanding understanding of their regularity properties and providing new classes of such maps.

Contribution

It introduces conditions for constructing real map germs with Milnor fibrations, regardless of Thom regularity, broadening the scope of known examples.

Findings

Established conditions for Milnor tube fibrations in real map germs.

Constructed classes of maps with and without Thom regularity.

Enhanced understanding of the relationship between regularity and fibrations.

Abstract

We find natural and convenient conditions which allow us to produce classes of genuine real map germs with Milnor tube fibration, either with Thom regularity or without it.