On Isolated Real Singularities II

TL;DR

This paper extends previous work to analyze real ADE-singularities, computing homology groups of Milnor fibers and addressing classification issues of simple real singularities.

Contribution

It applies earlier results to real ADE-singularities, enabling homology computations and advancing the classification of simple real singularities.

Findings

Homology groups of Milnor fibers for real ADE-singularities of curves are determined.

Results extend to higher codimension ADE-singularities, providing nearly complete classification.

Discussion on the classification problem of simple real singularities is included.

Abstract

In this article we apply the results in the article "On Isolated Real Singularities I" to the study of real $ADE$-singularities. We show that said results enables us to find the homology groups of the Milnor fibres of real $ADE$-singularities of curves. As a corollary we show how to deduce the same for $ADE$-singularities in higher codimension, giving an almost complete answer in this case. This is followed by a discussion of the classification problem of simple real singularities.