A challenge to 3-manifold topologists and group algebraists

TL;DR

This paper challenges 3-manifold topologists and group algebraists by highlighting the importance of solving specific, difficult problems in 3-manifold topology, emphasizing their fundamental role in advancing mathematics.

Contribution

It raises fundamental questions about hard-to-find instances of problems in 3-manifold topology, stressing their significance over general concepts.

Findings

Identifies key difficult problems in 3-manifold topology

Highlights the importance of specific problem instances

Encourages focus on complex, fundamental problems in mathematics

Abstract

This paper poses some basic questions about instances (hard to find) of a special problem in 3-manifold topology. "Important though the general concepts and propositions may be with the modern industrious passion for axiomatizing and generalizing has presented us...nevertheless I am convinced that the special problems in all their complexity constitute the stock and the core of mathematics; and to master their difficulty requires on the whole the harder labor." Hermann Weyl 1885-1955, cited in the preface of the first edition (1939) of \cite{whitehead1997}.