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

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Bibliographic Details
Main Author: Sasaki, Dounnu
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2022
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Ergodic theory
Fuchsian groups
Functions of a complex variable > Riemann surfaces > Fuchsian groups and automorphic functions. msc
Group theory and generalizations > Special aspects of infinite or finite groups > Hyperbolic groups and nonpositively curved groups. msc
Hyperbolic groups
Riemann surfaces
Intersection number
Surface group
Hyperbolic group
Geodesic current
Hyperbolic surface
Free group
Subset current
ISBN:1470453436, 9781470453435
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Table of Contents:
  • Introduction -- Subset Currents on Hyperbolic Groups -- Volume Functionals on Kleinian Groups -- Subgroups, Inclusion Maps and Finite Index Extension -- Intersection Number -- Intersection Functional on Subset Currents -- Projection from Subset Currents onto Geodesic Currents -- Denseness Property of Rational Subset Currents
  • Cover -- Title page -- Chapter 1. Introduction -- 1.1. Background -- 1.2. Main results -- 1.3. Future study -- 1.4. Organization of article -- 1.5. Acknowledgements -- Chapter 2. Subset Currents on Hyperbolic Groups -- 2.1. Space of subset currents on hyperbolic group -- 2.2. Measure theory background -- Chapter 3. Volume Functionals on Kleinian Groups -- Chapter 4. Subgroups, Inclusion Maps and Finite Index Extension -- 4.1. Natural continuous linear maps between subgroups -- 4.2. Finite index extension of functionals -- Chapter 5. Intersection Number -- 5.1. Intersection number of closed curves -- 5.2. Intersection number of surfaces -- 5.3. Continuous extension of intersection number -- Chapter 6. Intersection Functional on Subset Currents -- Chapter 7. Projection from Subset Currents onto Geodesic Currents -- 7.1. Construction of projection -- 7.2. Application of projection -- Chapter 8. Denseness Property of Rational Subset Currents -- 8.1. Denseness property of free groups -- 8.2. Approximation by a sequence of subgroups -- 8.3. Denseness property of surface groups -- Bibliography -- Index -- Back Cover