The loop group and the cobar construction

We prove that for any 1-reduced simplicial set X, Adams' cobar construction, 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.


Published in:
Proceedings of the American Mathematical Society, 138, 5, 1861-1876
Year:
2010
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 Record created 2009-03-13, last modified 2018-03-17

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