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Abstract:

For a discrete group G, we define the notion of G-II-algebra whose model is given by the graded group (πn(K))n≥1 corresponding to a topological space K on which G acts. This notion is a natural extension of the notion of II-algebra ([8]) and we use it to construct a spectral sequence relied to the II-algebra IImapGpt(X, Y), associated to the space of equivariant pointed continuous applications between two pointed G-CW-complexes X and Y. In particular, this spectral sequence converges to π*mapGpt(X, Y) when X is G-free and Y has only a finite number of non vanishing homotopy groups. We give an example obtained from the universal covering of BG.

Registro:

Documento: Artículo
Título:Une suite spectrale pour les groupes d'homotopie des espaces d'applications équivariantes
Autor:Fieux, E.; Solotar, A.
Filiación:Dto. de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Université Paris-Sud, Mathématiques, Batiment 425, 91405 Orsay CEDEX, France
Año:1998
Volumen:5
Número:4
Página de inicio:565
Página de fin:582
Título revista:Bulletin of the Belgian Mathematical Society - Simon Stevin
Título revista abreviado:Bull. Belg. Math. Soc. Simon Stevin
ISSN:13701444
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13701444_v5_n4_p565_Fieux

Referencias:

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  • Bousfield, A.K., Kan, D.M., A second quadrant homotopy spectral sequence (1973) TAMS, 177, pp. 305-318
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  • Dwyer, W.G., Kan, D.M., The envelopping ring of a II-algebra (1989) London Math. Soc. Lect. Note. Ser., 139, pp. 49-60. , Advances in Homotopy Theory
  • Dwyer, W.G., Kan, D.M., Homology and cohomology of II-algebras (1994) Trans. of the Am. Math. Soc., 342 (1), pp. 257-273
  • Dwyer, W.G., Kan, D.M., Smith, J.H., Stover, C.R., A II-algebra spectral sequence for function spaces (1994) Proc. of the Am. Math. Soc., 120 (2), pp. 615-621
  • Greenlees, J.P.C., Stable maps into free G-spaces (1988) Trans. of the Am. Math. Soc., 310 (2), pp. 199-215
  • Greenlees, J.P.C., May, J.P., Equivariant stable homotopy theory (1995) Handbook of Algebraic Topology, pp. 277-323. , (ed. by I.M. James), North Holland
  • Kan, D.M., A combinatorial definition of homotopy groups (1958) Annals of Math., 67 (2), pp. 287-312
  • Legrand, A., Homotopie des Espaces de Sections (1982) Lect. Notes in Math., 941
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Citas:

---------- APA ----------
Fieux, E. & Solotar, A. (1998) . Une suite spectrale pour les groupes d'homotopie des espaces d'applications équivariantes. Bulletin of the Belgian Mathematical Society - Simon Stevin, 5(4), 565-582.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13701444_v5_n4_p565_Fieux [ ]
---------- CHICAGO ----------
Fieux, E., Solotar, A. "Une suite spectrale pour les groupes d'homotopie des espaces d'applications équivariantes" . Bulletin of the Belgian Mathematical Society - Simon Stevin 5, no. 4 (1998) : 565-582.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13701444_v5_n4_p565_Fieux [ ]
---------- MLA ----------
Fieux, E., Solotar, A. "Une suite spectrale pour les groupes d'homotopie des espaces d'applications équivariantes" . Bulletin of the Belgian Mathematical Society - Simon Stevin, vol. 5, no. 4, 1998, pp. 565-582.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13701444_v5_n4_p565_Fieux [ ]
---------- VANCOUVER ----------
Fieux, E., Solotar, A. Une suite spectrale pour les groupes d'homotopie des espaces d'applications équivariantes. Bull. Belg. Math. Soc. Simon Stevin. 1998;5(4):565-582.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13701444_v5_n4_p565_Fieux [ ]