Volume 17, issue 1 (2013)

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

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Combinatorial group theory and the homotopy groups of finite complexes

Roman Mikhailov and Jie Wu

Geometry & Topology 17 (2013) 235–272
Bibliography
1 V G Bardakov, R Mikhailov, V V Vershinin, J Wu, Brunnian braids on surfaces, Algebr. Geom. Topol. 12 (2012) 1607 MR2966697
2 G Baumslag, Finitely presented groups, from: "Proc. Internat. Conf. Theory of Groups" (editors L G Kovacs, B H Neumann), Gordon and Breach (1967) 37 MR0215902
3 A J Berrick, F R Cohen, Y L Wong, J Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006) 265 MR2188127
4 A K Bousfield, E B Curtis, D M Kan, D G Quillen, D L Rector, J W Schlesinger, The mod p lower central series and the Adams spectral sequence, Topology 5 (1966) 331 MR0199862
5 R Brown, J L Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987) 311 MR899052
6 W L Chow, On the algebraical braid group, Ann. of Math. (2) 49 (1948) 654 MR0026050
7 F R Cohen, J Wu, On braid groups, free groups, and the loop space of the 2-sphere, from: "Categorical decomposition techniques in algebraic topology" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 93 MR2039761
8 F R Cohen, J Wu, Artin’s braid groups, free groups, and the loop space of the 2-sphere, Q. J. Math. 62 (2011) 891 MR2853222
9 D Conduché, Modules croisés généralisés de longueur 2, from: "Proceedings of the Luminy conference on algebraic K-theory" (editors E M Friedlander, M Karoubi) (1984) 155 MR772056
10 E B Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971) 107 MR0279808
11 G Ellis, R Mikhailov, A colimit of classifying spaces, Adv. Math. 223 (2010) 2097 MR2601009
12 A O Houcine, Embeddings in finitely presented groups which preserve the center, J. Algebra 307 (2007) 1 MR2278040
13 D M Kan, A combinatorial definition of homotopy groups, Ann. of Math. 67 (1958) 282 MR0111032
14 D M Kan, On homotopy theory and c.s.s. groups, Ann. of Math. 68 (1958) 38 MR0111033
15 D M Kan, W P Thurston, Every connected space has the homology of a K(π,1), Topology 15 (1976) 253 MR0413089
16 J Y Li, J Wu, On symmetric commutator subgroups, braids, links and homotopy groups, Trans. Amer. Math. Soc. 363 (2011) 3829 MR2775829
17 W Magnus, A Karrass, D Solitar, Combinatorial group theory : presentations of groups in terms of generators and relations, 13, Interscience Publishers (1966) MR0207802
18 R Mikhailov, I B S Passi, J Wu, Symmetric ideals in group rings and simplicial homotopy, J. Pure Appl. Algebra 215 (2011) 1085 MR2747240
19 J Milnor, On the construction F[K], from: "Algebraic topology—a student guide" (editor J F Adams), London Mathematical Society Lecture Note Series 4, Cambridge Univ. Press (1972) 119
20 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
21 J H C Whitehead, On the asphericity of regions in a 3–sphere, Fund. Math. 32 (1939) 149
22 J Wu, On combinatorial descriptions of homotopy groups and the homotopy theory of mod 2 Moore spaces, PhD thesis, University of Rochester (1995) MR2693367
23 J Wu, On fibrewise simplicial monoids and Milnor–Carlsson’s constructions, Topology 37 (1998) 1113 MR1650351
24 J Wu, Combinatorial descriptions of homotopy groups of certain spaces, Math. Proc. Cambridge Philos. Soc. 130 (2001) 489 MR1816806
25 J Wu, A braided simplicial group, Proc. London Math. Soc. 84 (2002) 645 MR1888426
26 H Zhao, X Wang, Combinatorial description of the homotopy groups of wedge of spheres, Proc. Amer. Math. Soc. 137 (2009) 371 MR2439462