Geometry & Topology Volume 26, issue 3 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Asymptotically rigid mapping class groups, I: Finiteness properties of braided Thompson's and Houghton's groups

Anthony Genevois, Anne Lonjou and Christian Urech

Geometry & Topology 26 (2022) 1385–1434

DOI: 10.2140/gt.2022.26.1385

Bibliography

1	J Aramayona, L Funar, Asymptotic mapping class groups of closed surfaces punctured along Cantor sets, Mosc. Math. J. 21 (2021) 1 MR4219034
2	J Belk, B Forrest, Rearrangement groups of fractals, Trans. Amer. Math. Soc. 372 (2019) 4509 MR4009393
3	J Belk, M C B Zaremsky, Twisted Brin–Thompson groups, Geom. Topol. 26 (2022) 1189
4	R W Bell, D Margalit, Braid groups and the co-Hopfian property, J. Algebra 303 (2006) 275 MR2253663
5	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
6	T Brady, J Burillo, S Cleary, M Stein, Pure braid subgroups of braided Thompson’s groups, Publ. Mat. 52 (2008) 57 MR2384840
7	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
8	M G Brin, Higher dimensional Thompson groups, Geom. Dedicata 108 (2004) 163 MR2112673
9	M G Brin, The algebra of strand splitting, I : A braided version of Thompson’s group V , J. Group Theory 10 (2007) 757 MR2364825
10	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
11	K S Brown, Finiteness properties of groups, J. Pure Appl. Algebra 44 (1987) 45 MR885095
12	K U Bux, Tangling and braiding the chessboard complex, preprint (2003) arXiv:math/0310420
13	K U Bux, Higher finiteness properties of braided groups, from: "Spectral structures and topological methods in mathematics" (editors M Baake, F Götze, W Hoffmann), Eur. Math. Soc. (2019) 299 MR4248149
14	K U Bux, Arc matching complexes and finiteness properties, Oberwolfach Rep. 17 (2021) 1121
15	K U Bux, M G Fluch, M Marschler, S Witzel, M C B Zaremsky, The braided Thompson’s groups are of type F_∞, J. Reine Angew. Math. 718 (2016) 59 MR3545879
16	F Degenhardt, Endlichkeitseigenschaften gewisser Gruppen von Zöpfen unendlicher Ordnung, PhD thesis, Goethe-Universität Frankfurt am Main (2000)
17	P Dehornoy, The group of parenthesized braids, Adv. Math. 205 (2006) 354 MR2258261
18	C Druţu, M Kapovich, Geometric group theory, 63, Amer. Math. Soc. (2018) MR3753580
19	S Eilenberg, Sur les transformations périodiques de la surface de sphère, Fund. Math. 22 (1934) 28
20	D S Farley, Homological and finiteness properties of picture groups, Trans. Amer. Math. Soc. 357 (2005) 3567 MR2146639
21	L Funar, Braided Houghton groups as mapping class groups, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. 53 (2007) 229 MR2386796
22	L Funar, C Kapoudjian, On a universal mapping class group of genus zero, Geom. Funct. Anal. 14 (2004) 965 MR2105950
23	L Funar, C Kapoudjian, The braided Ptolemy–Thompson group is finitely presented, Geom. Topol. 12 (2008) 475 MR2390352
24	L Funar, C Kapoudjian, The braided Ptolemy–Thompson group is asynchronously combable, Comment. Math. Helv. 86 (2011) 707 MR2803858
25	L Funar, C Kapoudjian, V Sergiescu, Asymptotically rigid mapping class groups and Thompson’s groups, from: "Handbook of Teichmüller theory, III" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 17, Eur. Math. Soc. (2012) 595 MR2952772
26	A Genevois, A Lonjou, C Urech, Asymptotically rigid mapping class groups, II: Strand diagrams and nonpositive curvature, preprint (2021) arXiv:2110.06721
27	A Genevois, A Lonjou, C Urech, Asymptotically rigid mapping class groups, III: Explicit presentations, in preparation
28	V Guba, M Sapir, Diagram groups, 620, Amer. Math. Soc. (1997) MR1396957
29	J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR786348
30	A Hatcher, On triangulations of surfaces, Topology Appl. 40 (1991) 189 MR1123262
31	G Higman, Finitely presented infinite simple groups, 8, Aust. Nat. Univ. (1974) MR0376874
32	C H Houghton, The first cohomology of a group with permutation module coefficients, Arch. Math. (Basel) 31 (1978) 254 MR521478
33	B Hughes, Local similarities and the Haagerup property, Groups Geom. Dyn. 3 (2009) 299 MR2486801
34	Y Lodha, J T Moore, A nonamenable finitely presented group of piecewise projective homeomorphisms, Groups Geom. Dyn. 10 (2016) 177 MR3460335
35	N Monod, Groups of piecewise projective homeomorphisms, Proc. Natl. Acad. Sci. USA 110 (2013) 4524 MR3047655
36	V V Nekrashevych, Cuntz–Pimsner algebras of group actions, J. Operator Theory 52 (2004) 223 MR2119267
37	B E A Nucinkis, S St. John-Green, Quasi-automorphisms of the infinite rooted 2–edge-coloured binary tree, Groups Geom. Dyn. 12 (2018) 529 MR3813202
38	C E Röver, Constructing finitely presented simple groups that contain Grigorchuk groups, J. Algebra 220 (1999) 284 MR1714140
39	R Skipper, S Witzel, M C B Zaremsky, Simple groups separated by finiteness properties, Invent. Math. 215 (2019) 713 MR3910073
40	M Stein, Groups of piecewise linear homeomorphisms, Trans. Amer. Math. Soc. 332 (1992) 477 MR1094555
41	W Thumann, Operad groups and their finiteness properties, Adv. Math. 307 (2017) 417 MR3590523
42	S Witzel, Classifying spaces from Ore categories with Garside families, Algebr. Geom. Topol. 19 (2019) 1477 MR3954289
43	S Witzel, M C B Zaremsky, Thompson groups for systems of groups, and their finiteness properties, Groups Geom. Dyn. 12 (2018) 289 MR3781423