On the Andrews-Curtis conjecture and algorithms from topology

2001/08/08 by Siddhartha Gadgil, Gadgil, Siddhartha
Mathematics · #20F05 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F05 #msc:57M07

paper · pdf · doi:10.48550/arxiv.math/0108053

12 pages, 7 figures

arxiv created 2001/08/08 · arxiv updated 2009/11/30

Abstract

We relate the Andrews-Curtis conjecture to the triviality problem for balanced presentations of groups using algorithms from 3-manifold topology. Implementing this algorithm could lead to counterexamples to the Andrews-Curtis conjecture.

Related

• The complexity of balanced presentations and the Andrews-Curtis conjecture
• Genetic algorithms and the Andrews-Curtis conjecture
• Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture
• On conjectures of Andrews and Curtis
• On the Andrews-Curtis equivalence