Algebraic & Geometric Topology Volume 19, issue 3 (2019)

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Classifying spaces from Ore categories with Garside families

Stefan Witzel

Algebraic & Geometric Topology 19 (2019) 1477–1524

DOI: 10.2140/agt.2019.19.1477

Bibliography

1	E Artin, Theorie der Zöpfe, Abh. Math. Sem. Univ. Hamburg 4 (1925) 47 MR3069440
2	J M Belk, Thompson’s group F, PhD thesis, Cornell University (2004) arXiv:0708.3609 MR2706280
3	J Belk, B Forrest, Rearrangement groups of fractals, preprint (2015) arXiv:1510.03133
4	J Belk, B Forrest, A Thompson group for the basilica, Groups Geom. Dyn. 9 (2015) 975 MR3428407
5	D Bessis, The dual braid monoid, Ann. Sci. École Norm. Sup. 36 (2003) 647 MR2032983
6	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
7	J S Birman, Braids, links, and mapping class groups, Princeton Univ. Press (1974) MR0375281
8	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
9	A Björner, L Lovász, S T Vrećica, R T Živaljević, Chessboard complexes and matching complexes, J. London Math. Soc. 49 (1994) 25 MR1253009
10	T Brady, A partial order on the symmetric group and new K(π,1)’s for the braid groups, Adv. Math. 161 (2001) 20 MR1857934
11	T Brady, J Burillo, S Cleary, M Stein, Pure braid subgroups of braided Thompson’s groups, Publ. Mat. 52 (2008) 57 MR2384840
12	E Brieskorn, K Saito, Artin-Gruppen und Coxeter-Gruppen, Invent. Math. 17 (1972) 245 MR0323910
13	M G Brin, Higher dimensional Thompson groups, Geom. Dedicata 108 (2004) 163 MR2112673
14	M G Brin, On the Zappa–Szép product, Comm. Algebra 33 (2005) 393 MR2124335
15	M G Brin, The algebra of strand splitting, I : A braided version of Thompson’s group V , J. Group Theory 10 (2007) 757 MR2364825
16	K S Brown, Finiteness properties of groups, J. Pure Appl. Algebra 44 (1987) 45 MR885095
17	K S Brown, R Geoghegan, An infinite-dimensional torsion-free FP_∞ group, Invent. Math. 77 (1984) 367 MR752825
18	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
19	J W Cannon, W J Floyd, W R Parry, Introductory notes on Richard Thompson’s groups, Enseign. Math. 42 (1996) 215 MR1426438
20	R Charney, J Meier, K Whittlesey, Bestvina’s normal form complex and the homology of Garside groups, Geom. Dedicata 105 (2004) 171 MR2057250
21	P Dehornoy, The group of parenthesized braids, Adv. Math. 205 (2006) 354 MR2258261
22	P Dehornoy, F Digne, E Godelle, D Krammer, J Michel, Foundations of Garside theory, 22, Eur. Math. Soc. (2015) MR3362691
23	D S Farley, Finiteness and CAT(0) properties of diagram groups, Topology 42 (2003) 1065 MR1978047
24	M G Fluch, M Marschler, S Witzel, M C B Zaremsky, The Brin–Thompson groups sV are of type F_∞, Pacific J. Math. 266 (2013) 283 MR3130623
25	F A Garside, The braid group and other groups, Quart. J. Math. Oxford Ser. 20 (1969) 235 MR0248801
26	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
27	G Higman, Finitely presented infinite simple groups, 8, Australian National University (1974) MR0376874
28	V F R Jones, A no-go theorem for the continuum limit of a periodic quantum spin chain, Comm. Math. Phys. 357 (2018) 295 MR3764571
29	C Kassel, V Turaev, Braid groups, 247, Springer (2008) MR2435235
30	D Kozlov, Combinatorial algebraic topology, 21, Springer (2008) MR2361455
31	C Martínez-Pérez, F Matucci, B E A Nucinkis, Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V , Forum Math. 28 (2016) 909 MR3543701
32	E Pardo, The isomorphism problem for Higman–Thompson groups, J. Algebra 344 (2011) 172 MR2831934
33	D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
34	D Quillen, Homotopy properties of the poset of nontrivial p–subgroups of a group, Adv. in Math. 28 (1978) 101 MR493916
35	R Skipper, S Witzel, M C B Zaremsky, Simple groups separated by finiteness properties, Invent. Math. 215 (2019) 713 MR3910073
36	M Stein, Groups of piecewise linear homeomorphisms, Trans. Amer. Math. Soc. 332 (1992) 477 MR1094555
37	W Thumann, Operad groups and their finiteness properties, Adv. Math. 307 (2017) 417 MR3590523
38	C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. 81 (1965) 56 MR0171284
39	C T C Wall, Finiteness conditions for CW complexes, II, Proc. Roy. Soc. Ser. A 295 (1966) 129 MR0211402
40	S Witzel, Finiteness properties of thompson groups, Habilitation, Bielefeld University (2016)
41	S Witzel, M C B Zaremsky, The Basilica Thompson group is not finitely presented, preprint (2016) arXiv:1603.01150
42	S Witzel, M C B Zaremsky, The Σ–invariants of Thompson’s group F via Morse theory, from: "Topological methods in group theory" (editors N. Broaddus, M. Davis, J F Lafont, I J Ortiz), London Mathematical Society Lecture Note Series 451, Cambridge Univ. Press (2018) 173
43	S Witzel, M C B Zaremsky, Thompson groups for systems of groups, and their finiteness properties, Groups Geom. Dyn. 12 (2018) 289 MR3781423