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June 1997 The self-equivalence groups in certain coherent homotopy categories
H.J. Baues, K.A. Hardie, K.H. Kamps
Tsukuba J. Math. 21(1): 213-228 (June 1997). DOI: 10.21099/tkbjm/1496163173

Abstract

We study the self-equivalence groups associated with objects in (i) the track homotopy category over a fixed space $B$, (ii) the track homotopy category under a fixed space $A$ and (iii) the category of homotopy pairs. In each case a short exact sequence decomposition of the self-equivalence group is available. In the case of (i) the group is isomorphic to the group of fibre-homotopy self-equivalences of an associated fibration, the decomposition (in other form) is known and has been used as the basis of computations. We make sample computations in the simplest situations for (i), (ii), and (iii), in each case solving the extension problem that arises by considering secondary operations and determining the Toda-Hopf invariant of relevant tracks. We indicate that in certain cases such computations can be used to determine the self-equivalence group of a mapping cone.

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H.J. Baues. K.A. Hardie. K.H. Kamps. "The self-equivalence groups in certain coherent homotopy categories." Tsukuba J. Math. 21 (1) 213 - 228, June 1997. https://doi.org/10.21099/tkbjm/1496163173

Information

Published: June 1997
First available in Project Euclid: 30 May 2017

zbMATH: 0883.55011
MathSciNet: MR1467233
Digital Object Identifier: 10.21099/tkbjm/1496163173

Rights: Copyright © 1997 University of Tsukuba, Institute of Mathematics

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Vol.21 • No. 1 • June 1997
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