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1999 Higher homotopy groupoids and Toda brackets
K. A. Hardie, K. H. Kamps, R. W. Kieboom
Homology Homotopy Appl. 1(1): 117-134 (1999).


We describe a category htTop whose objects are pointed continuous maps and whose morphisms are generated under composition by the tracks (relative homotopy classes) of homotopies. For example, if $m_t:hk\to *$ is a nullhomotopy then its track is a morphism from $k$ to $h$. The composition of tracks in htTop amounts to a sharpening of the classical secondary composition operation (Toda bracket). Standard properties of the Toda bracket can be derived in this setting. Moreover we show that htTop is itself the homotopy category of a bicategory htTop and so admits also a secondary composition operation.


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K. A. Hardie. K. H. Kamps. R. W. Kieboom. "Higher homotopy groupoids and Toda brackets." Homology Homotopy Appl. 1 (1) 117 - 134, 1999.


Published: 1999
First available in Project Euclid: 13 February 2006

zbMATH: 1002.55011
MathSciNet: MR1691710

Primary: 55Q05
Secondary: 18D05 , 55Q35 , 55U35

Rights: Copyright © 1999 International Press of Boston

Vol.1 • No. 1 • 1999
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