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.
Repository Citation
Lupton, Gregory and Smith, Samuel Bruce, "The Evaluation Subgroup of A Fibre Inclusion" (2007). Mathematics and Statistics Faculty Publications. 241.
https://engagedscholarship.csuohio.edu/scimath_facpub/241
DOI
10.1016/j.topol.2006.11.001
Version
Postprint
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Volume
154
Issue
6
