Contact Finite Determinacy of Relative Map Germs (Communications in Mathematical Research, 2021)
The strong contact finite determinacy of relative map germs is studied bymeans of classical singularity theory. We first give the definition of a strong relativecontact equivalence (or $\mathcal{K}_{S,T}$ equivalence) and then prove two theorems which canbe used to distinguish the contact finite determinacy of relative map germs, that is, $f$ is finite determined relative to $\mathcal{K}_{S,T}$ if and only if there exists a positive integer $k$,such that $\mathcal{M}^k(n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.
Keywords: $\mathcal{K}_{S; T}$ equivalent; the tangent space of an orbit; relative deformation; finite determined relative to $\mathcal{K}_{S; T}$