Relative Infinite Determinacy for Map-Germs

الملخص EN

The infinite determinacy for smooth map-germs with respect to two equivalence relations will be investigated.

We treat the space of smooth map-germs with a constraint, and the constraint is that a fixed submanifold in the source space is mapped into another fixed submanifold in the target space.

We study the infinite determinacy for such map-germs with respect to a subgroup of right-left equivalence group and finite and infinite determinacy with respect to a subgroup of contact group and give necessary and sufficient conditions for the corresponding determinacy.