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- W2798707919 abstract "We define the extra-nice dimensions and prove that the subset of locally stable 1-parameter families in $C^{infty}(Ntimes[0,1],P)$, also known as pseudo-isotopies, is dense if and only if the pair of dimensions $(dim N, dim P)$ is in the extra-nice dimensions. This result is parallel to Mather's characterization of the nice dimensions as the pairs $(n,p)$ for which stable maps are dense. The extra-nice dimensions are characterized by the property that discriminants of stable germs in one dimension higher have $mathcal A_e$-codimension 1 hyperplane sections. They are also related to the simplicity of $mathcal A_e$-codimension 2 germs. We give a sufficient condition for any $mathscr A_e$-codimension 2 germ to be simple and give an example of a corank 2 codimension 2 germ in the nice dimensions which is not simple. Then we establish the boundary of the extra-nice dimensions. Finally we answer a question posed by Wall about the codimension of non-simple maps." @default.
- W2798707919 created "2018-05-07" @default.
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- W2798707919 date "2018-04-25" @default.
- W2798707919 modified "2023-09-27" @default.
- W2798707919 title "The extra-nice dimensions" @default.
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