Geometry & Topology Volume 12, issue 1 (2008)

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The braided Ptolemy–Thompson group is finitely presented

Louis Funar and Christophe Kapoudjian

Geometry & Topology 12 (2008) 475–530

DOI: 10.2140/gt.2008.12.475

Bibliography

1	E Artin, Theory of braids, Ann. of Math. $(2)$ 48 (1947) 101 MR0019087
2	B Bakalov, A Kirillov Jr., On the lego-Teichmüller game, Transform. Groups 5 (2000) 207 MR1780935
3	V N Bezverkhniĭ, Solution of the generalized conjugacy problem for words in $C(p)&T(q)$–groups, Izv. Tul. Gos. Univ. Ser. Mat. Mekh. Inform. 4 (1998) 5 MR1751577
4	J Birman, K H Ko, S J Lee, A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998) 322 MR1654165
5	M G Brin, The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V arXiv:math.GR/0406042
6	M G Brin, The chameleon groups of Richard J. Thompson: automorphisms and dynamics, Inst. Hautes Études Sci. Publ. Math. (1996) MR1441005
7	K S Brown, Presentations for groups acting on simply-connected complexes, J. Pure Appl. Algebra 32 (1984) 1 MR739633
8	K U Bux, Braiding and tangling the chessboard complex arXiv:math.GT/0310420
9	D Calegari, Circular groups, planar groups, and the Euler class, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7, Geom. Topol. Publ., Coventry (2004) 431 MR2172491
10	J W Cannon, W J Floyd, W R Parry, Introductory notes on Richard Thompson's groups, Enseign. Math. $(2)$ 42 (1996) 215 MR1426438
11	F Degenhardt, Endlichkeitseigeinschaften gewiser Gruppen von Zöpfen unendlicher Ordnung, PhD thesis, Frankfurt (2000)
12	P Dehornoy, Geometric presentations for Thompson's groups, J. Pure Appl. Algebra 203 (2005) 1 MR2176650
13	P Dehornoy, The group of parenthesized braids, Adv. Math. 205 (2006) 354 MR2258261
14	P Dehornoy, I Dynnikov, D Rolfsen, B Wiest, Why are braids orderable?, Panoramas et Synthèses 14, Société Mathématique de France (2002) MR1988550
15	I A Dynnikov, Three-page representation of links, Uspekhi Mat. Nauk 53 (1998) 237 MR1691196
16	I A Dynnikov, Recognition algorithms in knot theory, Uspekhi Mat. Nauk 58 (2003) 45 MR2054090
17	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
18	D S Farley, Finiteness and $\mathrm CAT(0)$ properties of diagram groups, Topology 42 (2003) 1065 MR1978047
19	V Fock, Dual Teichmüller spaces arXiv:dg-ga/9702018
20	L Funar, R Gelca, On the groupoid of transformations of rigid structures on surfaces, J. Math. Sci. Univ. Tokyo 6 (1999) 599 MR1742596
21	L Funar, C Kapoudjian, The Ptolemy–Thompson group is asynchronously combable arXiv:math.GT/0602490
22	L Funar, C Kapoudjian, On a universal mapping class group of genus zero, Geom. Funct. Anal. 14 (2004) 965 MR2105950
23	S M Gersten, H Short, Small cancellation theory and automatic groups. II, Invent. Math. 105 (1991) 641 MR1117155
24	É Ghys, V Sergiescu, Sur un groupe remarquable de difféomorphismes du cercle, Comment. Math. Helv. 62 (1987) 185 MR896095
25	P Greenberg, V Sergiescu, An acyclic extension of the braid group, Comment. Math. Helv. 66 (1991) 109 MR1090167
26	R I Grigorchuk, V V Nekrashevich, V I Sushchanskiĭ, Automata, dynamical systems, and groups, Tr. Mat. Inst. Steklova 231 (2000) 134 MR1841755
27	V Guba, M Sapir, Diagram groups, Mem. Amer. Math. Soc. 130 (1997) MR1396957
28	C Kapoudjian, V Sergiescu, An extension of the Burau representation to a mapping class group associated to Thompson's group $T$, from: "Geometry and dynamics", Contemp. Math. 389, Amer. Math. Soc. (2005) 141 MR2181963
29	M Kontsevich, Y Soibelman, Affine structures and non-archimedean spaces arXiv:math.AG/0406564
30	P Lochak, L Schneps, The universal Ptolemy-Teichmüller groupoid, from: "Geometric Galois actions, 2", London Math. Soc. Lecture Note Ser. 243, Cambridge Univ. Press (1997) 325 MR1653018
31	A V Malyutin, Fast algorithms for the recognition and comparison of braids, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 279 (2001) 197, 250 MR1846081
32	D R Mason, On the $2$-generation of certain finitely presented infinite simple groups, J. London Math. Soc. $(2)$ 16 (1977) 229 MR0466324
33	J Matthews, The conjugacy problem in wreath products and free metabelian groups, Trans. Amer. Math. Soc. 121 (1966) 329 MR0193130
34	L Mosher, Mapping class groups are automatic, Ann. of Math. $(2)$ 142 (1995) 303 MR1343324
35	R C Penner, The universal Ptolemy group and its completions, from: "Geometric Galois actions, 2", London Math. Soc. Lecture Note Ser. 243, Cambridge Univ. Press (1997) 293 MR1653016
36	R C Penner, J L Harer, Combinatorics of train tracks, Annals of Mathematics Studies 125, Princeton University Press (1992) MR1144770
37	D J S Robinson, A course in the theory of groups, Graduate Texts in Mathematics 80, Springer (1996) MR1357169
38	V Sergiescu, Graphes planaires et présentations des groupes de tresses, Math. Z. 214 (1993) 477 MR1245207
39	B Wiest, Diagram groups, braid groups, and orderability, J. Knot Theory Ramifications 12 (2003) 321 MR1983088
40	D Witte, Arithmetic groups of higher $\mathbf{Q}$-rank cannot act on $1$-manifolds, Proc. Amer. Math. Soc. 122 (1994) 333 MR1198459