Bogomolov multipliers of groups
Presented by Primoz MORAVEC
Type: Oral presentation
Track: Plenary Talk
The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramiﬁed Brauer group of a given quotient space, and represents an obstruction to the problem of stable rationality of ﬁxed ﬁelds. In this talk we survey some recent results regarding Bogomolov multipliers. We derive a homological version of the Bogomolov multiplier, prove a Hopf-type formula, ﬁnd a ﬁve term exact sequence corresponding to this invariant, and describe the role of the Bogomolov multiplier in the theory of central extensions. An algorithm for computing the Bogomolov multiplier is developed. We deﬁne the Bogomolov multiplier within K-theory and show that proving its triviality is equivalent to solving a long-standing problem posed by Bass.