| 书目名称 | Ergodic Theoretic Methods in Group Homology |
| 副标题 | A Minicourse on L2-B |
| 编辑 | Clara Löh |
| 视频video | |
| 概述 | Makes recent developments on L2-Betti numbers of groups and related invariants easily accessible to advanced students and researchers.Explains the rich interplay between the residually finite approach |
| 丛书名称 | SpringerBriefs in Mathematics |
| 图书封面 |  |
| 描述 | This book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of .L.2.-Betti numbers..Group homology integrates group actions into homological structure. Coefficients based on probability measure preserving actions combine ergodic theory and homology. An example of such an interaction is provided by .L.2.-Betti numbers: these invariants can be understood in terms of group homology with coefficients related to the group von Neumann algebra, via approximation by finite index subgroups, or via dynamical systems. In this way, .L.2.-Betti numbers lead to orbit/measure equivalence invariants and measured group theory helps to compute .L.2.-Betti numbers. Similar methods apply also to compute the rank gradient/cost of groups as well as the simplicial volume of manifolds..This book introduces .L.2.-Betti numbers of groups at an elementary level and thendevelops the ergodic point of view, emphasising the connection with approximation phenomena for homological gradient invariants of groups and spaces. The text is an extended version of the lecture notes for a minicourse at the MSRI summer graduate school “Random and arithmetic struct |
| 出版日期 | Book 2020 |
| 关键词 | L2-Betti numbers; von Neumann dimension; measured group theory; approximation of homological invariants |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-44220-0 |
| isbn_softcover | 978-3-030-44219-4 |
| isbn_ebook | 978-3-030-44220-0Series ISSN 2191-8198 Series E-ISSN 2191-8201 |
| issn_series | 2191-8198 |
| copyright | The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 |
发表于 2025-3-21 16:17:37
