Document Type

Article

Publication Date

3-15-2007

Publication Title

Topology and Its Applications

Abstract

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.

DOI

10.1016/j.topol.2006.11.001

Version

Postprint

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Volume

154

Issue

6

Included in

Mathematics Commons

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