---
abstract: 'We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total “quantity” of singularity in the neighbourhood of infinity is related to the variation of topology in certain families of boundary singularities along the hyperplane at infinity.'
address:
- 'D.S.: Mathematisch Instituut, Universiteit Utrecht, PO Box 80010,  3508 TA Utrecht The Netherlands.'
- 'M.T.: Math'' ematiques, UMR-CNRS 8524, Université de Lille 1,   59655 Villeneuve d’Ascq, France.'
author:
- Dirk Siersma
- Mihai Tibăr
title: 'Deformations of polynomials, boundary singularities and monodromy'
---

Introduction
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One of the fundamental tools for studying singularities is deformation. In case of function germs with isolated singularity, classification and deformation results have been found through the pioneering work of V.I. Arnol’d in the early 1970s, one of the most spectacular being the list of simple singularities, their possible deformations and their amazing connections to other branches of mathematics [@Ar1]. More recently, in the 1990s, the study of the behaviour of polynomial functions at infinity lead to a new branch: singularities at infinity of polynomials. In his 1998 paper [@Ar2], Arnol’d gave a list of simple germs of fractions and polynomials at infinity, together with their 