Self fibre homotopy equivalences of fibred products
type: Item
instance of: scholarly article
title: Self fibre homotopy equivalences of fibred products
zbMATH Open document ID: 0964.55010
DOI: 10.1016/S0166-8641(98)00143-6
author: Petar Pavešić
published in: Topology and its Applications
publication date: 2001-07-13T00:00:00Z
review text: A product decomposition is given for the group \({\mathcal E}_B(X\times _BY)\) of based fibre homotopy self-equivalence classes of the fibred product \(X\times _BY\) of two CW fibrations \(X\to B\) and \(Y\to B\). A homotopy self-equivalence \(f:F\times G\to F\times G\) is reducible if the composites \(F\to F\times G\to F\times G\to F\) and \(G\to F\times G\to F\times G\to G\) are homotopy self-equivalences. Given that all the homotopy self-equivalences of the fibre \(F\times G\) of \(X\times _BY\to B\) are reducible, then \({\mathcal E}_B(X\times _BY)\cong {\mathcal E}_X(X\times _BY) . {\mathcal E}_Y(X\times _BY)\) where the two groups have trivial intersection. The result is proved in a more general categorical setting. Criteria for reducibility are given, as well as a number of special cases.
Mathematics Subject Classification ID: 55P10
zbMATH DE Number: 1421586
zbMATH Keywords: homotopy self-equivalences
reviewed by: John W. Rutter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1421586