Factor and normal subgroup theorems for lattices in products of groups

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Groups acting on manifolds: around the Zimmer program (2008, methodology): “This strategy has been applied in other contexts and is a major tool in the construction of simple groups with good geometric properties see [6, 24, 25, 36].”
Stabilizers of Ergodic Actions of Lattices and Commensurators (2013, background): “n the following sections. The Poisson boundary for Gand µis a (G,µ)-space. We include the deﬁnition for completeness but will not need to study the structure of such spaces. The reader is referred to [BS06] and [Cre11] for more information. Deﬁnition 2.26. Let Gbe a locally compact second countable ”
Simplicity and superrigidity of twin building lattices (2006, methodology): “The following result is a restatement of the normal subgroup theorem proved in [5] and [64], in the general framework of twin building lattices.”
Isometry groups of non‐positively curved spaces: discrete subgroups (2009, methodology): “One can adapt the entire proof to the present setting, but we propose an alternative line of reasoning using an amenability theorem from [4].”
Poisson-Furstenberg Boundaries, Large-scale Geometry and Growth of Groups (2011, methodology): “For application of this criterion, as well of the generalization of this criterion for the case of amenable extension see [58, 83, 17, 7].”