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Attaching cells to finite complexes, with an application to elliptic spaces

Published online by Cambridge University Press:  24 October 2008

Geoffrey M. L. Powell
Geoffrey M. L. Powell
Affiliation:
The Mathematical Institute, 24–29 St Giles', Oxford, OX1 3LB
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Extract

Suppose that f; Sn → E is a continuous map from the n-sphere to a 1-connected CW complex E, with n ≥ 2. One may suppose that f is a cofibration, so that there is a cofibration sequence , with f the attaching map of the cell en+1. Consider the homotopy fibre F of the inclusion E ↪ B, so that there is a homotopy fibration let δ; ΩB → F be the connectant of this fibration. The following definition is given by Félix and Lemaire in [11]: Definition 1·1. Suppose that k is a field of characteristic p ≥ 0. The attaching map f:Sn → E is: 1. p-inert if is surjective; 2. p-lazy if is zero; where H˜ denotes reduced homology and coefficients are taken in the field k.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 483 - 491
Copyright
Copyright © Cambridge Philosophical Society 1996

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