Classification of Equidimensional contact unimodular map germs.

Volume preserving subgroups of $${{\mathcal A}}$$ and $${{\mathcal K}}$$ and singularities in unimodular geometry

“…(and non-w.q.h.) map-germs f from the classifications in [14,15,51]. These results give upper bounds for dim M (K n , f ), and for certain f some of these upper bound will coincide with the following lower bound (which is analogous to Lemma 5.1 in the A p case).…”

“…Looking at the lists in [14,15,51] we see (using our results) that a K-unimodal map-germ f is w.q.h. for K n if and only if it is quasihomogeneous.…”

“…Notice that F W 1,1 (with µ(F 1,1 ) = 17 and τ (F 1,1 ) = 15) corresponds to the exceptional parameter λ = 0 in the modular stratum λ∈C\{0,−1/4} K · g λ (which seems to be missing in Wall's list) and does not lie in the closure of the orbit of F W 1,0 . Example 6.3 Consider the K-unimodal equidimensional maps of type h λ,q from [15], given by f = f λ := (xz + x y 2 + y 3 , yz, x 2 + y 3 + λz q ) = f 0 + (0, 0, y 3 + λz q ), q > 2.…”

On C1-stability and C1-determinacy

“…It follows at once from (0.4) B that no mapping in the T^oo-open subset ô fG^N, P) promised by Lemma (0.5) has all its point-germs oo-j^-determined, and the proof is complete. D All this is very abstract; but the results have a more concrete form arising from the calculations of ^{n^p) (carried out in [8], VI) and ^{n^p) (carried out in [25] for n> p, [4] for n = p, and [26] for n<p).…”

Simple singularities of space curves

“…We first obtained our list via rather explicit changes of co-ordinates, and lavish applications of the Mather Lemma. It was Bruce who pointed out to us that the method of ' complete transversals', introduced for Jf-classification in [6], extends to certain subgroups of si -in particular to the groups stf k of co-ordinate changes having fc-jet the identity [5]. That method allows a more efficient and natural derivation of the list.…”