Question de Whitehead et modules précroisés

Conduché, Daniel

Bulletin de la Société Mathématique de France, Tome 124 (1996) no. 3, pp. 401-423.

[1] Adams (J.F.). - A new proof of a theorem of W.H. Cockroft, J. London Math. Soc., t. 30, 1955, p. 482-488. | MR | Zbl

[2] Baer (R.). - Representations of groups as quotient groups III, Trans. A.M.S., t. 58, 1945, p. 390-419. | Zbl

[3] Baues (H.J.). - Algebraic homotopy. - Cambridge Studies on Advanced Mathematics 15, Cambridge University Press, Cambridge 1989. | MR | Zbl

[4] Baues (H.J.) and Conduché (D.). - The central series for Peiffer commutators in groups with operators, J. Algebra, t. 133, 1990, p. 1-34. | MR | Zbl

[5] Bogley (W.A.). - An embedding for π2 of a subcomplex of a finite contractible two-complex, Glasgow Math J., t. 33, 1991, p. 365-371. | MR | Zbl

[6] Bogley (W.A.). - On J.H.C. Whitehead's asphericity question in “Two-dimensional homotopy and combinatorial group theory”, C. Hog-Angeloni, W. Metzler and A.J. Sieradski editors. - London Math. Soc., Lecture Note Series 197, 1993, p. 309-334, Cambridge University Press, Cambridge. | MR | Zbl

[7] Bogley (W.A.) and Gutiérrez (M.A.). - Mayer-Vietoris sequences in homotopy of 2-complexes and in homology of groups, J. Pure Applied Algebra, t. 77, 1992, p. 39-65. | MR | Zbl

[8] Bourbaki (N.). - Algèbre commutative, chapitres I à IV. - Masson, Paris, 1985.

[9] Brandenburg (J.) and Dyer (M. N.). - On J.H.C. Whitehead's aspherical question I, Comm. Math. Helv., t. 56, 1981, p. 431-446. | MR | Zbl

[10] Brown (R.). - Coproducts of crossed P-module : Applications to second homotopy groups and to the homology of groups, Topology, t. 23, 1984, p. 337-345. | MR | Zbl

[11] Brown (R.) and Huebschmann (J.). - Identities among relations in “Low dimensional Topology”, R. Brown and T.L. Thickstun editors. - London Math. Soc. Lecture Note Series 48, 1982, p. 153-202, Cambridge University Press, Cambridge. | MR | Zbl

[12] Cockcroft (W.H.). - On two dimensional aspherical complexes, Proc. London Math. Soc., t. (3), 4, 1954, p. 375-384. | MR | Zbl

[13] Cohn (P. M.). - Generalization of a theorem of Magnus, Proc. London Math. Soc., t. (3), 2, 1952, p. 297-310. | MR | Zbl

[14] Conduché (D.). - Modules croisés généralisés de longueur 2, J. Pure Applied Algebra, t. 34, 1984, p. 155-178. | MR | Zbl

[15] Conduché (D.) et Ellis (G.J.). - Quelques propriétés homologiques des modules précroisés, J. Algebra, t. 123, 1989, p. 327-335. | MR | Zbl

[16] Curtis (E.B.). - Simplicial homotopy theory, Advances in Math., t. 6, 1971, p. 107-209. | MR | Zbl

[17] Dyer (M.N.). - Crossed Modules and π2 Homotopy Modules in “Two-dimensional homotopy and combinatorial group theory”, C. Hog-Angeloni, W. Metzler and A. J. Sieradski editors. - London Math. Soc. Lecture Note Series 197, 1993, p. 309-334, Cambridge University Press, Cambridge. | Zbl

[18] Dyer (M.N.). - Subcomplexes of two-complexe and projectives crossed modules in "Combinatorial Group Theory and Topology", S.M. Gersten and J. Stallings editors, Ann. of Math. Studies, t. 111, 1987, p. 255-264. | MR | Zbl

[19] Ellis (G.J.). - Homology of 2-types, J. London Math. Soc., t. 46, 1992, p. 1-27. | MR | Zbl

[20] Ellis (G.J.) and Porter (T.). - Free and projective crossed modules and the second homology group of a group, J. Pure Appl. Algebra, t. 40, 1986, p. 27-31. | MR | Zbl

[21] Gutiérrez (M.A.) and Ratcliffe (J.G.). - On the second homotopy group, Quart. J. Math. Oxford, t. (2), 32, 1981, p. 45-55. | MR | Zbl

[22] Howie (J.). - On locally indicable groups, Math. Z., t. 180, 1982, p. 445-461. | MR | Zbl

[23] Huebschmann (J.). - Aspherical 2-complexes and an unsettled problem of J.H.C. Whitehead, Math. Ann., t. 258, 1981, p. 17-37. | MR | Zbl

[24] Illusie (L.). - Complexe cotangent et déformation, tome 2. - Lecture Notes in Math. 283, Springer, Berlin, 1972. | MR | Zbl

[25] Kan (D.M.). - A relation between CW-complexes and free groups, Amer. J. Math., t. 81, 1959, p. 518-528. | MR | Zbl

[26] Lamotke (K.). - Semisimpliziale algebraische Topologie, Grundlehren der Math. Wiss., t. 167, Springer, Berlin, 1968. | MR | Zbl

[27] May (J.P.). - Simplicial objects in algebraic topology. - Math. Studies, 11, Van Nostrand, Princeton, 1967. | MR | Zbl

[28] Papakyriakopoulos (C.D.). - Attaching 2-dimensional cells to a complex, Ann. Math., t. 78, 1963, p. 205-222. | MR | Zbl

[29] Passi (I.B.S.). - Annihilators of relation modules II, J. Pure Appl. Algebra, t. 6, 1975, p. 235-237. | MR | Zbl

[30] Passman (D.S.). - The algebraic structure of group rings. - Pure and Appl. Math., vol. XX, J. Wiley and Sons, New York, 1979.

[31] Peiffer (R.). - Uber Identitäten zwischen Relationen, Math. Ann., t. 121, 1949, p. 67-99. | MR | Zbl

[32] Quillen (D.). - Spectral sequence of a double semi-simplicial group, Topology, t. 5, 1966, p. 155-157. | MR | Zbl

[33] Ratcliffe (J.G.). - Free and projective crossed modules, J. London Math. Soc., t. 22, 1980, p. 66-74. | MR | Zbl

[34] Stallings (J.). - Homology and Central series of groups, J. Algebra, t. 2, 1965, p. 770-787. | MR | Zbl

[35] Whitehead (J.H.C.). - On adding relations to homotopy groups, Ann. Math., t. 42, 1941, p. 409-428. | JFM | MR | Zbl

[36] Whitehead (J.H.C.). - Note on a previous paper intitled "On adding relations to homotopy groups", Ann. Math., t. 47, 1946, p. 806-810. | MR | Zbl