"Geometry and Analysis on Groups" Research Seminar
Time: 2018.04.10, 15:00–17:00
Location: Seminarraum 10, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "2D Problems in Groups."
Speaker: Aditi Kar
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 free-ness of modules over group rings. This is joint work with Nikolay Nikolov.