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
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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
AbstractList 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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Author Sasaki, Dounnu
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Keywords Intersection number
Surface group
Hyperbolic group
Geodesic current
Hyperbolic surface
Free group
Subset current
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Notes July 2022, volume 278, number 1368 (third of 6 numbers)
Includes bibliographical references (p. 163-164) and index
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Snippet Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic currents on hyperbolic groups, which were...
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SubjectTerms 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
TableOfContents 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
Title Subset currents on surfaces
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Volume 278
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