Steenrod problem and the domination relation

TL;DR

This paper combines classical and modern topology techniques to demonstrate that certain manifold maps must have degree zero, providing a homotopy theoretic interpretation involving Thom spaces and Steenrod powers.

Contribution

It introduces a novel approach linking Thom's work on the Steenrod problem with simplicial volume to analyze map degrees between manifolds.

Findings

Certain maps between manifolds must have degree zero

Homotopy theoretic interpretation using Thom spaces and Steenrod powers

New connections between classical and modern topology

Abstract

We indicate how to combine some classical topology (Thom's work on the Steenrod problem) with some modern topology (simplicial volume) to show that every map between certain manifolds must have degree zero. We furthermore discuss a homotopy theoretic interpretation of parts of our proof, using Thom spaces and Steenrod powers.