Disentanglements of maps from 2n-space to 3n-space

Kevin Houston

Vol. 218 (2005), No. 1, 115–137

DOI: 10.2140/pjm.2005.218.115

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 2000

Primary: 32S30, 32S55

Milestones

Received: 21 March 2002

Revised: 31 January 2003

Published: 1 January 2005