Simplicial groups as models for n-types
Cabello, J. G.
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997), p. 67-92 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{CTGDC_1997__38_1_67_0,
     author = {Cabello, J. G.},
     title = {Simplicial groups as models for $n$-types},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {38},
     year = {1997},
     pages = {67-92},
     mrnumber = {1437197},
     zbl = {0873.18004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_1997__38_1_67_0}
}

Cabello, J. G. Simplicial groups as models for $n$-types. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) pp. 67-92. http://gdmltest.u-ga.fr/item/CTGDC_1997__38_1_67_0/

[1] R. Brown and M. Golasinski, A model structure for the homotopy category of crossed complexes, Cahiers de Top. et Géom. Diff. Cat. 30 (1989), 61-82. | Numdam | MR 1000831 | Zbl 0679.55016

[2] J.G. Cabello, Estructuras de modelos de Quillen para categorías que modelan algebraicamente tipos de homotopía de espacios, Ph.D.thesis, Univ. Granada, (1993).

[3] J.G. Cabello and A.R. Carzon, Closed model structures for algebraic models of n-types, J. of Pure and Applied Algebra 103, (1995), 287-302. | MR 1357790 | Zbl 0837.55014

[4] J.G. Cabello and A.R. Garzon, Quillen's theory for algebraic model of n-types, Extracta Math. Vol 9, No 1, (1904), 42-48. | MR 1304150 | Zbl 1032.55500

[5] P. Carrasco and A.M. Cegarra, Group theoretic algebraic models for homotopy types, J. of Pure and Applied Algebra 75, (1991), 195-235. | MR 1137837 | Zbl 0742.55003

[6] S.E. Crans, Quillen closed model structures for sheaves, to appear in J. of Pure and Applied Algebra. | MR 1346427 | Zbl 0828.18005

[7] E.B. Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971), 107-209. | MR 279808 | Zbl 0225.55002

[8] S. Eilenberg and S. Mac Lane, Relatiotis between homology and homotopy groups, Proc. Nat. Acad. Sci. USA 29, (1943). | Zbl 0061.40701

[9] C. Elvira, L.J. Hernández, Closed model categories for the n-type of spaces and simplicial sels, Math. proc. Camb. Phil. Soc., (1995). | Zbl 0837.55013

[10] J.I. Extremiana, L.J. Hernández and M.T. Rivas, A closed model category for (n - 1)-connected spaces, preprint, (1995).

[11] P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy theory, Ergebnisse der Mathematik, vol. 35, Springer-Verlag, Berlin (1967). | MR 210125 | Zbl 0186.56802

[12] P. Glenn, Realization of cohomolgy classes in arbitrary exact categories, J. of Pure and Applied Algebra, 25, (1982), 33-107: | MR 660389 | Zbl 0487.18015

[13] P.J. Higgins, Groups with multiple operators, Proc. London Math. Soc. 6, (1956), 366-416. | MR 82492 | Zbl 0073.01704

[14] L. Hernández and T. Porter, Categorical models of n-types for pro-crossed complexes and Jn-spaces, L.N. in Math. 1509, (1992), 148-185. | Zbl 0752.55005

[15] D.M. Kan, On hnntntopy theory and CSS groups, Ann. of Math. 68, (1958), 38-53. | Zbl 0091.36902

[16] J.P. May, Simplicial objects in algebraic topology, Nostrand, New York, (1976). | MR 222892 | Zbl 0165.26004

[17] T. Porter, n-types of simplicial groups and crossed n-cubes, Topology 32, 1 (1993), 5-24. | MR 1204402 | Zbl 0776.55012

[18] D. Quillen, Homotopical Algebra, L.N. in Math 43, Springer (1967). | MR 223432 | Zbl 0168.20903

[19] D. Quimen, Rational Homotopy Theory, Ann. of Math. 90, (1969). | MR 258031 | Zbl 0191.53702

[20] J.H.C. Whitehead, Combinatorial Homotopy I and II, Bull. Amer. Soc. 55, (1949), 213-245 and 496-543. | MR 30759 | Zbl 0040.38704