A new test for asphericity and diagrammatic reducibility of group presentations
Group Theory
2016-10-06 v2 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1601.00604,
title = {A new test for asphericity and diagrammatic reducibility of group presentations},
author = {Jonathan Ariel Barmak and Elias Gabriel Minian},
journal= {arXiv preprint arXiv:1601.00604},
year = {2016}
}
Comments
We added a new section with applications to equations over groups