Bounded Cohomology and Simplicial Volume
Caterina Campagnolo ¡ Francesco Fournier-Facio ¡ Nicolaus Heuer ¡ Marco Moraschini
āĻ¨āĻā§ ā§¨ā§Ļā§¨ā§¨ ¡ London Mathematical Society Lecture Note Series āĻŦāĻ 479 ¡ Cambridge University Press
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Since their introduction by Gromov in the 1980s, the study of bounded cohomology and simplicial volume has developed into an active field connected to geometry and group theory. This monograph, arising from a learning seminar for young researchers working in the area, provides a collection of different perspectives on the subject, both classical and recent. The book's introduction presents the main definitions of the theories of bounded cohomology and simplicial volume, outlines their history, and explains their principal motivations and applications. Individual chapters then present different aspects of the theory, with a focus on examples. Detailed references to foundational papers and the latest research are given for readers wishing to dig deeper. The prerequisites are only basic knowledge of classical algebraic topology and of group theory, and the presentations are gentle and informal in order to be accessible to beginning graduate students wanting to enter this lively and topical field.
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Caterina Campagnolo is a postdoctoral researcher now working at UAM Madrid.
Francesco Fournier-Facio is PhD student at ETH ZÃŧrich.
Nicolaus Heuer received his PhD from the University of Oxford.
Marco Moraschini is a type A fixed-termed Researcher at University of Bologna. He was previously a Postdoctoral Researcher at University of Regensburg.
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