Topology and Its Applications
Let ξ: X j−→Ep−→B be a fibration of simply connected CW complexes of finite type with classifying map h: B→Baut1(X).We study the evaluation subgroup G n (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(h)Q=0.
Lupton, Gregory and Smith, Samuel Bruce, "The Evaluation Subgroup of A Fibre Inclusion" (2007). Mathematics Faculty Publications. 241.
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