An Invitation to Coarse Groups
This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms “up to uniformly bounded error”. These structures are the group objects in the category of coarse spaces, and arise naturally as approximate subgroups, or as coarse kernels. The fi...
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Springer Nature Switzerland : Imprint: Springer,
2023.
|
| Edisyon: | 1st ed. 2023. |
| Seri Bilgileri: | Lecture Notes in Mathematics,
2339 |
| Konular: | |
| Online Erişim: | https://doi.org/10.1007/978-3-031-42760-2 |
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| 100 | 1 | |a Leitner, Arielle. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 3 | |a An Invitation to Coarse Groups |h [electronic resource] / |c by Arielle Leitner, Federico Vigolo. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XV, 248 p. 8 illus.). |b 6 illus. in color. | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2339 | |
| 520 | |a This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms “up to uniformly bounded error”. These structures are the group objects in the category of coarse spaces, and arise naturally as approximate subgroups, or as coarse kernels. The first aim is to provide a standard entry-level introduction to coarse groups. Extra care has been taken to give a detailed, self-contained and accessible account of the theory. The second aim is to quickly bring the reader to the forefront of research. This is easily accomplished, as the subject is still young, and even basic questions remain unanswered. Reflecting its dual purpose, the book is divided into two parts. The first part covers the fundamentals of coarse groups and their actions. Here the theory of coarse homomorphisms, quotients and subgroups is developed, with proofs of coarse versions of the isomorphism theorems, and it is shown how coarse actions are related to fundamental aspects of geometric group theory. The second part, which is less self-contained, is an invitation to further research, where each thread leads to open questions of varying depth and difficulty. Among other topics, it explores coarse group structures on set-groups, groups of coarse automorphisms and spaces of controlled maps. The main focus is on connections between the theory of coarse groups and classical subjects, including: number theory; the study of bi-invariant metrics on groups; quasimorphisms and stable commutator length; groups of outer automorphisms; and topological groups and their actions. The book will primarily be of interest to researchers and graduate students in geometric group theory, topology, category theory and functional analysis, but some parts will also be accessible to advanced undergraduates. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
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| 588 | |a Print version record. | ||
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 1 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Topological Groups and Lie Groups. |
| 700 | 1 | |a Vigolo, Federico. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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