Vol. 84, No. 1, 1979

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Nonopenness of the set of Thom-Boardman maps

Leslie Wilson

Vol. 84 (1979), No. 1, 225–232

1. Introduction. In this paper, we show that the set of all C Thom-Boardman maps from an n-dimensional manifold is not open iff corank two singularities occur generically. The latter is known to occur iff either n p and 2p 3n 4 or n > p and 2p n + 4. In the course of the proof, we establish a variation of Mather’s Multitransversality Theorem: we show that jets have extensions which are multitransverse to given submanifolds of the jet bundle except possibly at the original jet. As an application of this extension theorem, we show that, in Mather’s “nice range of dimensions,” each iet z has a representative f(z = jkf(x)) such that f is infinitesimally stable on a deleted neighborhood of x.

Mathematical Subject Classification 2000
Primary: 58C27
Secondary: 57R45
Received: 18 July 1978
Revised: 9 February 1979
Published: 1 September 1979
Leslie Wilson