Hess, Kathryn
Tonks, Andrew
The loop group and the cobar construction
Proceedings of the American Mathematical Society
138
5
1861-1876
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.
Loop space;
cobar construction;
strong deformation retract;
acyclic models;
Differential Homological Algebra;
Perturbation-Theory;
2010
http://arxiv.org/abs/0903.1651;
http://infoscience.epfl.ch/record/134804/files/proc10238.pdf;