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Hairdressing in groups: a survey of combings and formal languages

Sarah Rees

Geometry & Topology Monographs 1 (1998) 493–509

DOI: 10.2140/gtm.1998.1.493

Bibliography
1 A V Aho, Indexed grammars—an extension of context-free grammars, J. Assoc. Comput. Mach. 15 (1968) 647–671 MR0258547
2 A V Aho, Nested stack automata, J. Assoc. Comput. Mach. 16 (1969) 383–406 MR0267980
3 G Baumslag, S M Gersten, M Shapiro, H Short, Automatic groups and amalgams, J. Pure Appl. Algebra 76 (1991) 229–316 MR1147304
4 G Baumslag, D Gildenhuys, R Strebel, Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras I, J. Pure Appl. Algebra 39 (1986) 53–94 MR816890
5 G Baumslag, M Shapiro, H Short, Parallel poly-pushdown groups, J. Pure Appl. Algebra 140 (1999) 209–227 MR1704452
6 N Brady, The geometry of asynchronous automatic structures on groups, PhD thesis, University of California, Berkeley (1993)
7 M R Bridson, On the geometry of normal forms in discrete groups, Proc. London Math. Soc. (3) 67 (1993) 596–616 MR1238046
8 M R Bridson, Combings of semidirect products and 3–manifold groups, Geom. Funct. Anal. 3 (1993) 263–278 MR1215781
9 M R Bridson, R H Gilman, Formal language theory and the geometry of 3–manifolds, Comment. Math. Helv. 71 (1996) 525–555 MR1420509
10 B Brink, R B Howlett, A finiteness property and an automatic structure for Coxeter groups, Math. Ann. 296 (1993) 179–190 MR1213378
11 J Burillo, Lower bounds of isoperimetric functions for nilpotent groups, from: "Geometric and computational perspectives on infinite groups (Minneapolis, MN and New Brunswick, NJ, 1994)", DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Amer. Math. Soc. (1996) 1–8 MR1364176
12 J W Cannon, The combinatorial structure of cocompact discrete hyperbolic groups, Geom. Dedicata 16 (1984) 123–148 MR758901
13 R Charney, Artin groups of finite type are biautomatic, Math. Ann. 292 (1992) 671–683 MR1157320
14 R Charney, Geodesic automation and growth functions for Artin groups of finite type, Math. Ann. 301 (1995) 307–324 MR1314589
15 D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett Publishers (1992) MR1161694
16 B Farb, Automatic groups: a guided tour, Enseign. Math. (2) 38 (1992) 291–313 MR1189009
17 S M Gersten, Bounded cocycles and combings of groups, Internat. J. Algebra Comput. 2 (1992) 307–326 MR1189238
18 S M Gersten, H B Short, Small cancellation theory and automatic groups, Invent. Math. 102 (1990) 305–334 MR1074477
19 R H Gilman, Formal languages and infinite groups, from: "Geometric and computational perspectives on infinite groups (Minneapolis, MN and New Brunswick, NJ, 1994)", DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Amer. Math. Soc. (1996) 27–51 MR1364178
20 R H Gilman, A shrinking lemma for indexed languages, Theoret. Comput. Sci. 163 (1996) 277–281 MR1407027
21 R H Gilman, D F Holt, S Rees, Combing nilpotent and polycyclic groups, Internat. J. Algebra Comput. 9 (1999) 135–155 MR1703070
22 T Hayashi, On derivation trees of indexed grammars: an extension of the uvwxy–theorem, Publ. Res. Inst. Math. Sci. 9 (1973/74) 61–92 MR0416123
23 J E Hopcroft, J D Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley Publishing Co., Reading, MA (1979) MR645539 Addison-Wesley Series in Computer Science
24 A Juhász, Large Artin groups are biautomatic, preprint
25 O G Harlampovič, A finitely presented solvable group with unsolvable word problem, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981) 852–873 MR631441
26 U Lang, Quasigeodesics outside horoballs, Geom. Dedicata 63 (1996) 205–215 MR1413632
27 L Mosher, Mapping class groups are automatic, Ann. of Math. (2) 142 (1995) 303–384 MR1343324
28 D Peifer, Artin groups of extra-large type are biautomatic, J. Pure Appl. Algebra 110 (1996) 15–56 MR1390670
29 M O Rabin, Real time computation, Israel J. Math. 1 (1963) 203–211 MR0163849
30 S Rees, Automatic groups associated with word orders other than shortlex, Internat. J. Algebra Comput. 8 (1998) 575–598 MR1675014
31 S Rees, A language theoretic analysis of combings, from: "Groups, languages and geometry (South Hadley, MA, 1998)", Contemp. Math. 250, Amer. Math. Soc. (1999) 117–136 MR1732211
32 D J S Robinson, Splitting theorems for infinite groups, from: "Symposia Mathematica, Vol XVII (Convegno sui Gruppi Infiniti, INDAM, Rome, 1973)", Academic Press (1976) 441–470 MR0407153
33 A L Rosenberg, Real-time definable languages, J. Assoc. Comput. Mach. 14 (1967) 645–662 MR0234783