Volume 12, issue 1 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The braided Ptolemy–Thompson group is finitely presented

Louis Funar and Christophe Kapoudjian

Geometry & Topology 12 (2008) 475–530
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