The evaluation subgroup of a fibre inclusion |
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Authors: | Gregory Lupton |
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Affiliation: | a Department of Mathematics, Cleveland State University, Cleveland, OH 44115, USA b Department of Mathematics, Saint Joseph's University, Philadelphia, PA 19131, USA |
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Abstract: | Let be a fibration of simply connected CW complexes of finite type with classifying map . We study the evaluation subgroup Gn(E,X;j) of the fibre inclusion as an invariant of the fibre-homotopy type of ξ. For spherical fibrations, we show the evaluation subgroup may be expressed as an extension of the Gottlieb group of the fibre sphere provided the classifying map h induces the trivial map on homotopy groups. We extend this result after rationalization: We show that the decomposition G∗(E,X;j)⊗Q=(G∗(X)⊗Q)⊕(π∗(B)⊗Q) is equivalent to the condition Q(h?)=0. |
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Keywords: | 55P62 55R15 55Q70 |
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