Deep pockets in lattices and other groups

Deep Pockets in Lattices and Other Groups

We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol’skĭi. We then give examples of important groups (namely lattices in Nil and Sol) which have deep pockets.

Repeated Interaction, Deep Pockets, and Litigation Spending

Decisions on litigation spending can be viewed as constituting an iterated nonzero sum game, and thus as conducive to cooperation aimed at reducing spending. At the same time, though, litigants may engage in aggressive spending for various reasons, including a belief that they can outsmart the other party. This article uses a litigation simulation to consider how litigation spending is affected...

Designs, Groups and Lattices

Symmetric Groups and Lattices

This paper deals with various problems in lattice theory involving local extrema. In particular, we construct infinite series of highly symmetric spherical 3-designs which include some of the examples constructed in [9] in dimensions 5 and 7. We also construct new types of dual-extreme lattices. Résumé. Quelques applications de l’algorithme de Voronöı équivariant. Nous considérons dans cet arti...

Free Groups in Lattices

Let G be any locally compact metrizable group. The main result of this paper, roughly stated, is that if F < G is any finitely generated free group and Γ < G any lattice, then up to a small perturbation and passing to a finite index subgroup, F is a subgroup of Γ. If G/Γ is noncompact then we require additional hypotheses that include G = SO(n, 1). MSC: 20E07, 20F65, 20F67, 22D40, 20E05.