Vol. 93, No. 2, 1981

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Jets with regular zeros

Leslie Wilson

Vol. 93 (1981), No. 2, 471–478
Abstract

If a mapgerm f : Rn, 0 Rp, 0 is a submersion (rkf = p), then its zero set is regular (the germ of a manifold) by the Implicit Function Theorem. Of course, there are also critical maps (rkf < p) whose zero sets are manifolds. Submersions have the added feature that one can discern that the zero set is regular from the first derivative of f at 0. Are there other instances in which one can tell purely from the derivatives of f at 0 that the zero set is regular? In this paper we show that there are, and go part way toward the eventual goal of describing them all.

Mathematical Subject Classification
Primary: 58C27
Milestones
Received: 27 August 1979
Revised: 2 June 1980
Published: 1 April 1981
Authors
Leslie Wilson