Abstract
We introduce the notion of versal unfoldings of germs of maps—unfoldings which, up to A-equivalence, explore all nearby possibilities of deformation. We prove Martinet’s theorem that infinitesimal versality is equivalent to versality, and use this to characterise versality in terms of transversality to orbits in jet space. We define bifurcation sets and prove their analyticity, and characterise Mather’s nice dimensions as those dimensions in which the bifurcation set is always a proper subset of the base space of a versal unfolding.
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Mond, D., Nuño-Ballesteros, J.J. (2020). Versal Unfoldings. In: Singularities of Mappings. Grundlehren der mathematischen Wissenschaften, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-030-34440-5_5
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DOI: https://doi.org/10.1007/978-3-030-34440-5_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34439-9
Online ISBN: 978-3-030-34440-5
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