Some applications for Fadell-Dold theorm in fibration theory by using homotopy groups

Details Some applications for Fadell-Dold theorm in fibration theory by using homotopy groups Some applications for Fadell-Dold theorm in fibration theory by using homotopy groups

2010-08-24

arxiv.org/abs/1008.3956v1

Mathematics

Algebraic Topology

18 pages, 8 figures

Scientific paper

The purpose of this paper is to give some solutions for the classification problem in fibration theory by using the homotopy sequences of fibrations (sequences of $n$-th homotopy groups $ \pi_{n}(S,s_{o}) $ of total spaces of fibrations). In particular, to show the role of homotopy sequence of $n$-th homotopy to get the required fiber map in Fadell-Dold theorem such that the restriction of this fiber map on some fiber spaces is a homotopy equivalence.

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