Relations among characteristic classes and existence of singular maps

TL;DR

This paper explores the relationships between characteristic classes of manifolds with corank one maps, providing restrictions on cobordism classes and nonexistence results for certain singular maps, using blow-up and perturbation techniques.

Contribution

It introduces new relations among characteristic classes for manifolds admitting corank one maps and derives nonexistence results for singular maps of projective spaces.

Findings

Restrictions on cobordism classes of manifolds

Nonexistence results for singular maps of projective spaces

Relations among characteristic classes derived from blow-up techniques

Abstract

We obtain relations among the characteristic classes of a manifold M admitting corank one maps. Our relations yield strong restrictions on the cobordism class of M and also nonexistence results for singular maps of the projective spaces. We obtain our results through blowing up a manifold along the singular set of a smooth map and perturbing the arising non-generic corank one map.