Complex monodromy and the topology of real algebraic sets

TL;DR

This paper explores the relationship between complex monodromy and real algebraic topology, specifically analyzing Euler characteristics of real Milnor fibers and links, revealing their modular properties.

Contribution

It introduces a novel connection between complex monodromy and real algebraic set topology, extending known results to iterated links of algebraic subsets.

Findings

Euler characteristic of real Milnor fibers relates to complex monodromy and conjugation

The link's Euler characteristic is generically constant modulo 4

Generalization to iterated links of algebraic subsets

Abstract

We study the Euler characteristic of the real Milnor fibres of a real analytic map, using a relation between complex monodromy and complex conjugation. We deduce the result of Coste and Kurdyka that the Euler characteristic of the link of an irreducible algebraic subset of a real algebraic set is generically constant modulo 4. We generalize this result to iterated links of ordered families of algebraic subsets.