The total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial

TL;DR

This paper provides a concrete formula for the total Milnor number of weighted-Le-Yomdin-at-infinity polynomials and describes their monodromy fibration at infinity, advancing understanding of their topological properties.

Contribution

It introduces a specific formula for the total Milnor number of these polynomials and characterizes their monodromy fibration at infinity, which was previously less understood.

Findings

Concrete formula for the total Milnor number in most cases

Description of the monodromy fibration at infinity

Enhanced understanding of the topology of weighted-Le-Yomdin-at-infinity polynomials

Abstract

We give a concrete formula for the total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial in most of the interesting cases. As an application, we give a description of the monodromy fibration at infinity for such kind of polynomial.