Abstract:
(BG) (Bounded Generation) of a group G by a subset U (symmetric, with unit) means the existence of a natural number N such that the map U^N->G given by N-time multiplication is surjective. In 1999, Shalom revealed a connection between (BG) and fixed point properties, such as (an equivalent formulation of) Kazhdan's property (T). However, (BG) hypothesis is super-strong in general... Later, Dymara--Januszkiewicz (2002) and then Ershov--Jaikin-Zapirain (2010) succeeded in bypassing (BG) by employing extrinsic data on group actions.
In this talk, I present the first answer to a natural question that asks whether it is possible to remove (BG) hypothesis from the original direction of Shalom, namely, from "intrinsic upgrading of fixed points."
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