Geometry & Topology Volume 17, issue 1 (2013)

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

Combinatorial group theory and the homotopy groups of finite complexes

Roman Mikhailov and Jie Wu

Geometry & Topology 17 (2013) 235–272

DOI: 10.2140/gt.2013.17.235

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