Topology Seminar

The stable Andrews-Curtis conjecture remains one of the most notorious unsolved problems in group theory. It proposes that every balanced presentation of the trivial group can reduced to the standard presentation (with one generator and one relation) using a sequence of simple moves. In my talk, I will focus on group presentations that are ‘thickenable’, which means that their associated 2-complex embeds in a 3-manifold. For such presentations, the stable Andrews-Curtis conjecture is known to hold. In my talk, I will explain how one can also get an explicit exponential-type upper bound on the number of stable Andrews-Curtis moves that are required. This is in sharp contrast to what is known about non-thickenable presentations.