Bounded Cohomology and Simplicial Volume

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.

自1980年代Gromov引入有界上同调和单纯体体积的研究以来，这一领域已经发展成为与几何和群论相关的活跃领域。本专著源于一个为在该领域工作的年轻研究人员举办的学习研讨会，提供了对该主题的不同视角的集合，包括经典和最新的观点。本书的引言部分介绍了有界上同调和单纯体体积理论的主要定义，概述了它们的历史，并解释了它们的主要动机和应用。接下来的各章节介绍了理论的不同方面，重点放在例子上。对于希望深入研究的读者，提供了对基础论文和最新研究的详细参考。前提只需要对经典代数拓扑和群论有基本的了解，而且呈现方式温和和不正式，以便初级研究生能够进入这个活跃和前沿的领域。