Algebra seminar

30 January 2018
Nikolay Nikolov
I will discuss a conjecture about stabilisation of deficiency in finite index subgroups and relate it to the D2 Problem of C.T.C. Wall and the Relation Gap problem for group presentations.
We can prove the pro-$p$ version of the conjecture, as well as its higher dimensional abstract analogues. Key ingredients are, first a classic result of Wall on the existence of CW complexes with prescribed cellular chain complex, and second, a simple criterion for freeness of modules over group rings. This is joint work with Aditi Kar.