On the topology of non-isolated real singularities

Nicolas Dutertre

Journal of Singularities
volume 22 (2020), 159-179

Received: 17 January 2019. Received in revised form: 21 June 2019.

DOI: 10.5427/jsing.2020.22j

Add a reference to this article to your citeulike library.

Abstract:

Khimshiashvili proved a topological degree formula for the Euler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As corollaries we obtain an algebraic formula for the Euler characteristic of the fibres of a real weighted-homogeneous polynomial and a real version of the Lê-Iomdine formula. We have also included some results of the same flavor on the local topology of locally closed definable sets.

2010 Mathematical Subject Classification:

32B05, 58K05, 58K65

Key words and phrases:

Topological degree, Euler characteristic, Real Milnor fibres

Author(s) information:

Nicolas Dutertre
Laboratoire angevin de recherche en mathématiques, LAREMA
UMR6093, CNRS, UNIV. Angers, SFR MathStic
2 Bd Lavoisier
49045 Angers Cedex 01, France
email: nicolas.dutertre@univ-angers.fr