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Handbook of group actions V. (English) Zbl 1439.14001

Advanced Lectures in Mathematics (ALM) 48. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-390-6/pbk). xi, 484 p. (2020).

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Publisher’s description: Groups are fundamental objects in mathematics, as they are responsible for the symmetries of any object or system under consideration. The presence of symmetry makes a problem more interesting and, as a general rule, easier to solve. In all cases, it is group action which makes groups useful and important. This is not surprising, since the notion of group was first introduced through group actions as permutation groups on roots of algebraic equations. On the other hand, the single notion of group action includes many different actions arising from various sources.
All of which is amply illustrated by the papers collected in this volume, the fifth Handbook of Group Actions. Topics include: classical geometric groups, geometric group theory, diffeomorphism groups of manifolds, mapping class groups, three-dimensional topology, hyperbolic manifolds, automorphism groups of complex manifolds, dynamics, and number theory.
For Vol. I–IV see [Zbl 1314.00005; Zbl 1314.00004; Zbl 1404.14004; Zbl 1404.14005].
The articles of this volume will be reviewed individually.
Indexed articles:
Ahumada, Guido; Brighi, Bernard; Chevallier, Nicolas; Fruchard, Augustin, Fixating group actions, 1-54 [Zbl 1458.51009]
Ceccherini-Silberstein, Tullio; Coornaert, Michel, The Garden of Eden theorem: old and new, 55-106 [Zbl 1456.37018]
Dani, Pallavi, The large-scale geometry of right-angled Coxeter groups, 107-141 [Zbl 07274139]
Hensel, Sebastian, A primer on handlebody groups, 143-177 [Zbl 07274140]
Kharlampovich, Olga; Vdovina, Alina, Beyond Serre’s “Trees” in two directions: \(\Lambda\)-trees and products of trees, 179-222 [Zbl 07274141]
Koberda, Thomas, Actions of right-angled Artin groups in low dimensions, 223-256 [Zbl 1455.57030]
Kutzschebauch, Frank, Manifolds with infinite dimensional group of holomorphic automorphisms and the linearization problem, 257-300 [Zbl 1453.32026]
Otera, Daniele Ettore; Poénaru, Valentin, Topics in geometric group theory. I, 301-346 [Zbl 1464.57034]
Poénaru, Valentin, Topics in geometric group theory. II, 347-398 [Zbl 07274145]
Pollicott, Mark, Dynamical zeta functions and the distribution of orbits, 399-440 [Zbl 1522.37038]
Seade, José, Kleinian groups in several complex variables, 441-476 [Zbl 1486.32008]

MSC:

14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry
14L30 Group actions on varieties or schemes (quotients)
13A50 Actions of groups on commutative rings; invariant theory
20-06 Proceedings, conferences, collections, etc. pertaining to group theory
57-06 Proceedings, conferences, collections, etc. pertaining to manifolds and cell complexes
20F38 Other groups related to topology or analysis
20F65 Geometric group theory
57M60 Group actions on manifolds and cell complexes in low dimensions
00B15 Collections of articles of miscellaneous specific interest
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