The vector field problem for homogeneous spaces

TL;DR

This survey explores the classical vector field problem within the context of compact homogeneous spaces, highlighting key topological challenges and known results in differential topology.

Contribution

It provides a comprehensive overview of the vector field problem specifically for compact homogeneous spaces, summarizing existing knowledge and open questions.

Findings

Summarizes known results on vector fields on compact homogeneous spaces.

Identifies key topological obstructions to the existence of vector fields.

Highlights open problems and directions for future research.

Abstract

The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.