Search

We present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails. We use this criterion to generalize results of J. Howie and S.M. Gersten on asphericity of LOTs and of Adian presentations, and derive new results on solvability of equations over groups. We also use our methods to investigate a conjecture of S.V. Ivanov related to Kaplansky's problem on zero divisors: we strengthen Ivanov's result for locally indicable groups and prove a weak version of the conjecture.

The question of whether ribbon-disc complements—or, equivalently, standard 2-complexes over labelled oriented trees—are aspherical is of great importance for Whitehead’s asphericity conjecture and, if solved affirmatively, would imply a combinatorial proof of the asphericity of knot complements. We present here two classes of diagrammatically reducible labelled oriented trees.

AMS 2000 Mathematics subject classification: Primary 57M20; 20F06; 20F05; 20F32

Search Results

Refine search

Refine search

Actions for selected content:

2 results

A new test for asphericity and diagrammatic reducibility of group presentations

ASPHERICAL LABELLED ORIENTED TREES AND KNOTS

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

A new test for asphericity and diagrammatic reducibility of group presentations

ASPHERICAL LABELLED ORIENTED TREES AND KNOTS