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H-Semidirect Products

Published online by Cambridge University Press:  20 November 2018

Georg Peschke
Georg Peschke*
Affiliation:
University of Calgary Calgary, Alberta, CanadaT2N 1N4
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Abstract

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The concept of H-semidirect product structure on a grouplike space is introduced. It is shown that the loop space ΩX of any based CW-complex X is the H-semidirect product of the identity path-component of ΩX with π1,X. The set of free homotopy classes of maps into a Hsemidirect product inherits the structure of a semidirect product. This leads to new results concerning the nilpotency of homotopy classes of maps into a group-like space.

Keywords

55D3555D4555E0555E35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 402 - 411
Copyright
Copyright © Canadian Mathematical Society 1987

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