The Development of the Theory of Automatic Groups

DOI10.1007/978-3-030-97560-9_14OpenAlexW4289535298MaRDI QIDQ5055450

Sarah Rees

Publication date: 13 December 2022

Published in: In the Tradition of Thurston II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.14911

zbMATH Keywords

3-manifold groupword problemCoxeter groupmapping class grouphyperbolic groupdecision problemfinite state automatonconjugacy problemautomatic groupArtin groupcombing

Mathematics Subject Classification ID

Geometric group theory (20F65) Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67) Group actions on manifolds and cell complexes in low dimensions (57M60) Turing machines and related notions (03D10) Classical models of computation (Turing machines, etc.) (68Q04)

Uses Software

• GAP
• Magma
• kbmag

Cites Work

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• Buildings with isolated subspaces and relatively hyperbolic Coxeter groups.
• The isomorphism problem for all hyperbolic groups.
• Small cancellation theory and automatic groups
• Artin groups and infinite Coxeter groups
• Small cancellation theory and automatic groups. II
• Artin groups of finite type are biautomatic
• Simplicial nonpositive curvature
• The combinatorial structure of cocompact discrete hyperbolic groups
• Automatic groups and amalgams
• The use of Knuth-Bendix methods to solve the word problem in automatic groups
• The word problem for Artin groups of FC type
• A finiteness property and an automatic structure for Coxeter groups
• Graph groups are biautomatic
• Algorithms and geometry for graph products of groups
• Formal language theory and the geometry of 3-manifolds
• Central quotients of biautomatic groups
• The geometry of cube complexes and the complexity of their fundamental groups
• Combings of groups and the grammar of reparameterization.
• Three-generator Artin groups of large type are biautomatic
• Combinatorial group theory.
• Automatic groups: A guided tour
• Quasigeodesics outside horoballs
• The isomorphism problem for hyperbolic groups. I
• Strongly geodesically automatic groups are hyperbolic
• Artin groups of extra-large type are biautomatic
• The Dehn function of \(\text{SL}(n;\mathbb Z)\).
• Helly meets Garside and Artin
• Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).
• Sol Geometry Groups are not Asynchronously Automatic
• THE CONJUGACY PROBLEM IN HYPERBOLIC GROUPS FOR FINITE LISTS OF GROUP ELEMENTS
• Shortlex automaticity and geodesic regularity in Artin groups
• RELATIVELY HYPERBOLIC GROUPS
• Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices
• Groups, Languages and Automata
• Groupes de Garside
• Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Coxeter Groups act on CAT(0) cube complexes
• POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)_∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN
• COMPUTATIONAL PROBLEMS IN HYPERBOLIC GROUPS
• COMPUTATION IN WORD-HYPERBOLIC GROUPS
• Semihyperbolic Groups
• An Alternative Proof That the Fibonacci Group F(2, 9) is Infinite
• Large‐type Artin groups are systolic
• Reflection triangles in Coxeter groups and biautomaticity
• THE LINEARITY OF THE CONJUGACY PROBLEM IN WORD-HYPERBOLIC GROUPS
• Indexed Grammars—An Extension of Context-Free Grammars
• CONJUGACY OF FINITE SUBSETS IN HYPERBOLIC GROUPS
• Mapping class groups are automatic

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