Some homotopy theoretical questions arising in Nielsen coincidence theory

TL;DR

This paper explores deep homotopy theoretical questions in Nielsen coincidence theory, highlighting connections to differential topology invariants and posing open questions for future research.

Contribution

It reviews recent results linking Nielsen coincidence theory with advanced homotopy invariants and raises new questions for further investigation.

Findings

Coincidence theory relates to Kervaire invariants and Whitehead products.

Recent results connect Nielsen theory with divisibility properties of homotopy invariants.

Open questions identified for advancing understanding in the field.

Abstract

Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seems to be important for a more comprehensive understanding.