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Proceedings of the American Mathematical Society

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Homology of a fibration over an aspherical space

Author: Yasutoshi Nomura
Journal: Proc. Amer. Math. Soc. 34 (1972), 527-533
MSC: Primary 55F05
MathSciNet review: 0296944
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Abstract: The aim of this paper is to establish, for a fibration over a space of type (Q, 1), an exact sequence involving the homology homomorphisms induced by the projection. Specializing to the case where the total space is aspherical, our sequence allows us to add some extra terms to the Eckmann-Stammbach exact sequence for a group extension with simple integer coefficient.

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  • [1] B. Eckmann and P. J. Hilton, Operators and cooperators in homotopy theory, Math. Ann. 141 (1960), 1–21 (1960). MR 0115162
  • [2] Beno Eckmann and Urs Stammbach, On exact sequences in the homology of groups and algebras, Illinois J. Math. 14 (1970), 205–215. MR 0269720
  • [3] Tudor Ganea, Homologie et extensions centrales de groupes, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A556–A558 (French). MR 0231914
  • [4] Yasutoshi Nomura, The Whitney join and its dual, Osaka J. Math. 7 (1970), 353–373. MR 0281208
  • [5] -, Homology of a group extension, Pacific J. Math. (submitted).
  • [6] Josef Schmid, Zu den Reduktionssätzen in der homologischen Theorie der Gruppen, Arch. Math. (Basel) 15 (1964), 28–32 (German). MR 0161896
  • [7] U. Stammbach, Anwendungen der Holomogietheorie der Gruppen auf Zentralreihen und auf Invarianten von Präsentierungen, Math. Z. 94 (1966), 157–177 (German). MR 0201495

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Keywords: Homology group, fibration, aspherical space, homology of a group, group extension, Whitney join, cofibre
Article copyright: © Copyright 1972 American Mathematical Society