On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

2010/08/24 by Amin Saif, Adem Kilicman, Adem Kılıçman +2
Mathematics · #55P10 #55P40 #55Q05 #55R10 #55U10 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Base (topology) #Combinatorics #Composite material #Computer science #FOS: Mathematics #Fiber #Fiber bundle #Fibration #Function (biology) #Homotopy #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Materials science #Mathematical analysis #Mathematics #Polyhedron #Pure mathematics #Space (punctuation) #math.AT #math.KT #msc:55P10 #msc:55P40 #msc:55Q05 #msc:55R10 #msc:55U10

paper · pdf · doi:10.48550/arxiv.1008.3959

17 pages, 2 figures

arxiv created 2010/08/24 · openalex publication_date 2010/08/24 · arxiv updated 2010/08/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let f:E\longrightarrow O be a Hurewicz fibration with a fiber space F_r_o and a lifting function L_f. The Lf-function Θ_L_f of f is defined by the restriction map of L_f on the space Ω(O,r_o)× F_r_o× \1\. The purpose of this paper is to give some results which show the role of Lf-functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of polyhedron spaces.

Citations

• An index theorem for Wiener–Hopf operators

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