Cobordisms of maps with singularities of a given class

2007/07/30 by Ando, Yoshifumi
#57R45 #57R90 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0707.4329

Abstract

Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given cal K-invariant class in terms of certain stable homotopy groups by applying the relative homotopy principle on the existence level. We also deal with the oriented version and construct a classifying space to which this oriented cobordism group is represented as the set of homotopy classes of P in the codimension n

Related

• Cobordisms of maps without prescribed singularities
• Smooth maps with singularities of bounded K-codimensions
• Cobordism of singular maps
• Cobordisms of singular maps
• Cobordism categories of manifolds with Baas-Sullivan singularities, Part 2