Titlebook: In the Tradition of Thurston III; Geometry and Dynamic Ken’ichi Ohshika,Athanase Papadopoulos Book 2024 The Editor(s) (if applicable) and T

Migratory

,Thurston’s Broken Windows Only Theorem Revisited,for Haken manifolds. In this chapter, we show that the second statement of this theorem is not valid, giving a counter-example. We also give a weaker version of this statement with a proof. In the last section, we speculate on how this second statement was intended to be used in the proof of the bou

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Counting Problems for Invariant Point Processes,the plane using an axiomatic perspective. Applications include counting holonomies of saddle connections, lattice points, and fine scale distribution in various contexts. This is a perspective inspired by work of Veech (Ann. Math. (2) 148(3):895–944, 1998), and developed further by, among others, Es

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Orbifolds and the Modular Curve,of view on the subject (discrete groups acting properly and effectively on differentiable manifolds), the construction of the modular orbi-curve and its universal family of elliptic curves ends up requiring a bit more technology, in order to allow for non-effective actions.

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Fecal-Impaction

language with dense choices gives rise to the latter. We also consider the nondeterministic random assignment and parallel composition, both couched in a simple language. Besides non determinism our four example languages contain some form of recursion, a key ingredient of programming languages.

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