New techniques for classification of multigerms (Q1688227)

This is a survey paper on the classification of multigerms. The authors give an overview on the state of art of the subject, describing the advances in the theory along the last 15 years. They describe new operations to obtain germs in certain dimensions from germs with fewer branches in lower dimensions. These new techniques were introduced to classify multigerms of \(\mathcal A_e\)-codimension 1 by \textit{T. Cooper} et al. [Compos. Math. 131, No. 2, 121--160 (2002; Zbl 1002.32016)] and applied to the classification of \(\mathcal A_e\)-codimension 2 multigerms by \textit{R. O. Sinha} et al. [Math. Z. 278, No. 1--2, 547--573 (2014; Zbl 1302.32026)]. The authors review these results and discuss how they apply to the classification of \(\mathcal A\)-simple germs. Various examples illustrating the classifications are given.