TY - EJOUR
AB - 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.
T1 - The loop group and the cobar construction
IS - 5
DA - 2010
AU - Hess, Kathryn
AU - Tonks, Andrew
JF - Proceedings of the American Mathematical Society
SP - 1861-1876
VL - 138
EP - 1861-1876
ID - 134804
KW - Loop space
KW - cobar construction
KW - strong deformation retract
KW - acyclic models
KW - Differential Homological Algebra
KW - Perturbation-Theory
UR - http://arxiv.org/abs/0903.1651
UR - http://infoscience.epfl.ch/record/134804/files/proc10238.pdf
ER -