Abstract: The classification and the geometry of corank 1 map germs f:(ℂ2, 0)→(ℂ3, 0) have been studied by David Mond. Normal forms of such maps f(x, y)=(x, p(x, y), q(x, y)) suggest, at least in some cases, that they could be seen as 1-parameter unfoldings of the plane curves γx(y)=(p(x, y), q(x, y)). If a certain genericity condition is satisfied, then the transverse slice curve γ0 contains information on the geometry of f. We introduce invariants C, J, T related to the Reidemeister moves (codimension 1 transitions) that appear in a stable perturbation of γ0. We compare them with Mond's invariants of f and obtain interesting geometric results. For instance, f is finitely determined if and only if C, J, T<∞ and given a 1-parameter family ft, it is Whitney equisingular if and only if the three invariants are independent of t.
Publication Year: 2014
Publication Date: 2014-02-23
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 15
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