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Examples of Finitely Determined Map-Germs of Corank 3 Supporting Mond's μ ⩾ τ-Type Conjecture

ABSTRACT In this paper, we give the first set of examples of finitely determined map-germs of corank 3 from 3-space to 4-space satisfying a conjecture by Mond that states the following. The number of parameters needed for a miniversal unfolding of a finitely determined map-germ from n-space to (n + 1)-space is less than (or equal to if the map-germ is weighted homogeneous) the rank of the nth homology group of the image of a stable perturbation of the map-germ, provided (n, n + 1) is in the range of Mather's nice dimensions. We describe some invariants of the multiple point spaces of one of our examples.