This monograph presents an overview of bounded cohomology, simplicial volume, and related topics, covering the basics of the subject and recent research directions. Aimed at graduate students entering the field, it includes precise definitions and many concrete examples while keeping an informal style and minimising prerequisites.
This monograph presents an overview of bounded cohomology, simplicial volume, and related topics, covering the basics of the subject and recent research directions. Aimed at graduate students entering the field, it includes precise definitions and many concrete examples while keeping an informal style and minimising prerequisites.
Introduction Caterina Campagnolo, Francesco Fournier-Facio, Nicolaus Heuer, Marco Moraschini Part I. Simplicial Volume: 1. Gromov's mapping theorem via multicomplexes Marco Moraschini 2. The proportionality principle via hyperbolic geometry Filippo Sarti 3. Positivity of simplicial volume via barycentric techniques Shi Wang 4. Gromov's systolic inequality via smoothing Lizhi Chen Integral foliated simplicial volume Caterina Campagnolo 6. l2-Betti numbers Holger Kammeyer Part II. Bounded Cohomology: 7. Stable commutator length Nicolaus Heuer 8. Quasimorphisms on negatively curved groups Biao Ma 9. Extension of quasicocycles from hyperbolically embedded subgroups Francesco Fournier-Facio 10. Lie groups and Symmetric spaces Anton Hase 11. Continuous bounded cohomology, representations and multiplicative constants Alessio Savini 12. The proportionality principle via bounded Filippo Baroni References Index.
Introduction Caterina Campagnolo, Francesco Fournier-Facio, Nicolaus Heuer, Marco Moraschini Part I. Simplicial Volume: 1. Gromov's mapping theorem via multicomplexes Marco Moraschini 2. The proportionality principle via hyperbolic geometry Filippo Sarti 3. Positivity of simplicial volume via barycentric techniques Shi Wang 4. Gromov's systolic inequality via smoothing Lizhi Chen Integral foliated simplicial volume Caterina Campagnolo 6. l2-Betti numbers Holger Kammeyer Part II. Bounded Cohomology: 7. Stable commutator length Nicolaus Heuer 8. Quasimorphisms on negatively curved groups Biao Ma 9. Extension of quasicocycles from hyperbolically embedded subgroups Francesco Fournier-Facio 10. Lie groups and Symmetric spaces Anton Hase 11. Continuous bounded cohomology, representations and multiplicative constants Alessio Savini 12. The proportionality principle via bounded Filippo Baroni References Index.
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