A lower bound on the top Betti number of the Milnor fiber

TL;DR

This paper establishes a lower bound for the highest non-zero Betti number of Milnor fibers using the zero-dimensional Lê number and internal monodromy, advancing understanding of their topological complexity.

Contribution

It introduces a new lower bound relating the top Betti number of Milnor fibers to Lê numbers and monodromy, providing deeper insight into their topology.

Findings

Derived a lower bound for the top Betti number of Milnor fibers.

Connected the Betti number to zero-dimensional Lê number and monodromy.

Enhanced understanding of the topological invariants of Milnor fibers.

Abstract

We derive a lower bound for the top possibly-non-zero Betti number of the Milnor fiber of an analytic function in terms of the zero-dimensional L\^e number and the internal monodromy of the vanishing cycles restricted to the complex link of the critical locus of the function.