Mathematics – Algebraic Topology
Scientific paper
2009-03-09
Mathematics
Algebraic Topology
14 pages
Scientific paper
We prove that for any 1-reduced simplicial set X, Adams' cobar construction, \Omega CX, on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX, opening up the possibility of applying the tools of homological algebra to transfering perturbations of algebraic structure from the latter to the former. In order to prove our theorem, we extend the definition of the cobar construction and actually obtain the existence of such a strong deformation retract for all 0-reduced simplicial sets.
Hess Kathryn
Tonks Andrew
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