Homotopy classification of multiply based textures

TL;DR

This paper demonstrates that the homotopy classification of multiply based textures on physical domains with multiple ends can be simplified to that on compact domains when the target space is simply connected, with applications to the O(3) sigma model.

Contribution

It establishes a reduction method for homotopy classification of textures with multiple ends to compact domains for simply connected target spaces.

Findings

Homotopy classification reduces to compact domains for simply connected targets.

Application to the O(3) sigma model on a cylinder.

Simplifies analysis of textures with multiple ends.

Abstract

It is shown that the homotopy classification of textures defined on physical domains with multiple ends at infinity reduces to that of textures on compact domains if the target space is simply connected. The result is applied to the O(3) sigma model on a cylinder, recently studied by Romao.