A Formula For the Homology Groups of the Milnor Fibres of an Isolated Real Hypersurface Singularity

TL;DR

This paper derives a formula to compute the singular homology groups of Milnor fibres associated with real hypersurface singularities, especially when the zero locus has positive dimension.

Contribution

It provides a new explicit formula for the homology groups of Milnor fibres in the context of real hypersurface singularities with positive-dimensional zero loci.

Findings

Derived a formula for homology groups of Milnor fibres

Applicable to polynomials with positive-dimensional zero locus

Advances understanding of real hypersurface singularities

Abstract

Given a nonconstant polynomial map over the reals having an isolated critical point in the origin and with zero locus of positive dimension, we establish a formula for the singular homology groups of a Milnor fibre relative to its boundary.