Bifurcations of polynomial maps with diffeomorphic and connected fibers

TL;DR

This paper demonstrates polynomial maps with a regular bifurcation value where, in a neighborhood, the fibers remain connected and diffeomorphic, revealing new insights into the structure of such maps.

Contribution

It introduces polynomial maps with regular bifurcation values that maintain connected and diffeomorphic fibers nearby, a novel property in the study of polynomial maps.

Findings

Existence of polynomial maps with regular bifurcation values

Fibers are connected and diffeomorphic near the bifurcation value

Advances understanding of polynomial map fiber structures

Abstract

We show the existence of polynomial maps which have a regular bifurcation value, while over a neighbourhood of this value the fibres are connected and diffeomorphic.