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245 10 a| Subset currents on surfacesh| [electronic resource] /c| Dounnu Sasaki.;

260 a| Providence, RI :b| American Mathematical Society,c| 2022.;

300 a| v, 165 pagesb| illustrationsc| 26 cm;

334 a| single unitb| mono0| http://id.loc.gov/vocabulary/issuance/mono;

340 p| illustrations0| http://id.loc.gov/vocabulary/millus/ill;

353 a| bibliographyb| bibliography0| http://id.loc.gov/vocabulary/msupplcont/bibliography;

353 a| indexb| index0| http://id.loc.gov/vocabulary/msupplcont/index;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 278, Number 1368 (third of 6 numbers);

504 a| Includes bibliographical references and index.;

506 a| Available only to authorized users.;

520 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()"-- Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Fuchsian groups0| http://id.loc.gov/authorities/subjects/sh92000719=| ^A368317;

650 0 a| Riemann surfaces0| http://id.loc.gov/authorities/subjects/sh85114044=| ^A33857;

650 0 a| Hyperbolic groups0| http://id.loc.gov/authorities/subjects/sh89006986=| ^A262584;

650 0 a| Ergodic theory0| http://id.loc.gov/authorities/subjects/sh85044600=| ^A15765;

650 7 a| Group theory and generalizations -- Special aspects of infinite or finite groups -- Hyperbolic groups and nonpositively curved groups2| msc;

650 7 a| Functions of a complex variable -- Riemann surfaces -- Fuchsian groups and automorphic functions2| msc;

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Subset currents on surfaces / Dounnu Sasaki.

Author/creator	Sasaki, Dounnu, 1990
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2022.
Description	v, 165 pages illustrations 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Fuchsian groups Riemann surfaces Hyperbolic groups Ergodic theory

Physical medium	illustrations
Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 278, Number 1368 (third of 6 numbers)
Abstract	"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()"-- Provided by publisher.
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022027944
ISBN	9781470453435 paperback
ISBN	pdf

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