Abstract

The first disentanglement of a multigerm f : (C²ⁿ,S) → (C³ⁿ,0) is shown to be homotopically equivalent to a wedge of (n + 1)-spheres and 2-spheres. For corank-1 monogerms in the same dimensions, the second disentanglement is shown to be homotopically equivalent to a wedge of n-spheres and circles.

Good real perturbations of such maps are investigated and it is shown for multigerms in the case n = 1 with a good real perturbation that the real and complex disentanglements are homotopically equivalent.

Mathematical Subject Classification

Primary: 32S30, 32S55

Authors