Subset currents on surfaces

Subset currents on surfaces

Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic currents on hyperbolic groups, which were introduced by Bonahon and have been successfully studied in the case of the fundamental group 1() of a compact hyperbolic surface . Kapovich and Na...

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Auteur principal : Sasaki Dounnu (Auteur)
Format : Livre
Langue : anglais
Titre complet : Subset currents on surfaces / Dounnu Sasaki
Publié : Providence (R.I.) : American Mathematical Society , C 2022
Description matérielle : 1 vol. (V-165 p.)
Collection : Memoirs of the American Mathematical Society ; 1368
Sujets :
Groupes fuchsiens
Riemann, Surfaces de
Groupes hyperboliques
Théorie ergodique
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330 |a Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic currents on hyperbolic groups, which were introduced by Bonahon and have been successfully studied in the case of the fundamental group 1() of a compact hyperbolic surface . Kapovich and Nagnibeda particularly studied subset currents on free groups. In this article, we develop the theory of subset currents on 1(), which we call subset currents on . We prove that the space SC() of subset currents on is a measure-theoretic completion of the set of conjugacy classes of non-trivial finitely generated subgroups of 1(), each of which geometrically corresponds to a convex core of a covering space of . This result was proved by Kapovich-Nagnibeda in the case of free groups, and is also a generalization of Bonahon's result on geodesic currents on hyperbolic groups. We will also generalize several other results of them. Especially, we extend the (geometric) intersection number of two closed geodesics on to the intersection number of two convex cores on and, in addition, to a continuous R0-bilinear functional on SC()  |2 résumé de l'auteur 
359 2 |b Chapter 1. Introduction  |b Chapter 2. Subset currents on hyperbolic groups  |b Chapter 3. Volume functionals on Kleinian groups  |b Chapter 4. Subgroups, inclusion maps and finite index extension  |b Chapter 5. Intersection number  |b Chapter 6. Intersection functional on subset currents  |b Chapter 7. Projection from subset currents onto geodesic currents  |b Chapter 8. Denseness property of rational subset currents  |b Bibliography  |b Index 
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