Computing Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups

We study homological Bogomolov multipliers and finitary Bogomolov multipliers of infinite groups, with emphasis on polycyclic groups. We obtain structural descriptions for torsion-free nilpotent groups of class two, semidirect products, wreath products, and infinite simple groups. The class-two case reveals a connection with rational points on linear sections of Grassmannians, explaining an arithmetic obstruction to a general algorithm. On the positive side, we give a deterministic algorithm for virtually abelian polycyclic groups and an algorithm for finitary Bogomolov multipliers of arbitrary polycyclic groups, both implemented in GAP.