Maps of manifolds of the same dimension with prescribed Thom-Boardman singularities

2018/10/25 by Ryabichev, Andrey
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1810.10990

Abstract

In this paper we extend Y.Eliashberg's h-principle to arbitrary generic smooth maps of smooth manifolds. Namely, we prove a necessary and sufficient condition for a continuous map of smooth manifolds of the same dimension to be homotopic to a generic map with a prescribed Thom-Boardman singularity Σ^I at each point. In dimension 3 we rephrase these conditions in terms of the Stiefel-Whitney classes and the cohomology classes of the given loci of folds, cusps and swallowtail points.

Related

• Cobordisms of maps without prescribed singularities
• Regular homotopy classes of locally generic mappings
• Realizing a homology class of a compact manifold by a homology class of an explicit closed submanifold--a new approach to Thom's works on homology classes of submanifolds-
• Regular homotopy classes of singular maps
• Special generic maps and Gromoll filtration