The extra-nice dimensions

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Date(s) - 22/03/2018
14 h 00 min - 15 h 00 min

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We define the extra-nice dimensions and prove that the subset of stable 1-parameter families in C∞(N × [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 Ae-codimension 1 hyperplane sections. They are also related to the simplicity of Ae-codimension 2 germs. We give a sufficient condition for any Ae-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.
This is a joint work with Raul Oset-Sinha (Valencia) and Roberta Wik Atique (ICMC-USP).

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