2002/10/17 by Javier Fernández de Bobadilla, J. Fernandez de Bobadilla, de Bobadilla, J. Fernandez
Computer Science · Mathematics · #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.AG #math.CV #msc:32S15 #msc:58K40
paper · pdf · doi:10.48550/arxiv.math/0210266
26 pages; Main Theorem improved
arxiv created 2002/12/11 · arxiv updated 2009/11/30
We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the following statement which generalizes classical results of Thom and Varchenko: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged under a deformation within the ideal that only modifies sufficiently large order terms of the Taylor expansion; then A has infinite codimension in I in a suitable sense. We also prove the existence of generic topological types of families of germs of I parametrized by an irreducible analytic set.