A stable range description of the space of link maps

TL;DR

This paper characterizes the space of link maps by identifying a dimension range where the cobordism class of the linking manifold fully determines the homotopy class of the link map, advancing understanding of link map classification.

Contribution

It provides a dimension range where the cobordism class of the linking manifold suffices to classify link maps up to homotopy, offering new insights into link map invariants.

Findings

Identifies a specific dimension range for link maps where cobordism class is a complete invariant.

Establishes a connection between linking manifold cobordism and homotopy classification.

Enhances the theoretical framework for understanding link map spaces.

Abstract

We study the space of link maps, which are smooth maps from the disjoint union of manifolds P and Q to a manifold N such that the images of P and Q are disjoint. We give a range of dimensions, interpreted as the connectivity of a certain map, in which the cobordism class of the "linking manifold" is enough to distinguish the homotopy class of one link map from another.