Simplicity of augmentations of codimension 1 germs and by Morse functions

2022/03/17 by Ignacio Breva Ribes, Ribes, I. Breva, R. Oset Sinha +1 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2203.09223

Abstract

We study the simplicity of map-germs obtained by the operation of augmentation and describe how to obtain their versal unfoldings. When the augmentation comes from an \mathscrA_e-codimension 1 germ or the augmenting function is a Morse function, we give a complete characterisation for simplicity. These characterisations yield all the simple augmentations in all explicitly obtained classifications of \mathscrA-simple monogerms except for one (F₄ in Mond's list from ℂ² to ℂ³). Moreover, using our results we produce a list of simple augmentations from ℂ⁴ to ℂ⁴.

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