On generalizations of the Milnor number
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
Matthias ZACH (Leibniz Universtät Hannover)
The Milnor number is central to the consideration of Isolated Hypersurface Singularities (IHS). It is both of topological and analytical nature as it describes the rank of the vanishing homology as well as the length of the space of infinitesimal deformations up to R-equivalence.
There are various generalizations of the Milnor number beyond the IHS case such as the L\^e-Greuel formula for ICIS. Another instance is the Euler obstruction of a map investigated by Seade, Tib\u ar and Verjovsky. A priori, this is based on a topological construction, but by virtue of the ideas around the "homological index" described by Ebeling, Gusein-Zade and Seade, analytic formulas for its computation become available. We shall use these to describe ways to determine the vanishing topology of Isolated Relative Complete Intersection Singularities (IRCIS).
- Matthias ZACH