134804
20181203021508.0
000276643400035
ISI
ARTICLE
The loop group and the cobar construction
2010
2010
Journal Articles
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
Hess, Kathryn
105396
240499
Tonks, Andrew
1861-1876
5
Proceedings of the American Mathematical Society
138
URL
http://arxiv.org/abs/0903.1651
Postprint
247711
Postprint
http://infoscience.epfl.ch/record/134804/files/proc10238.pdf
UPHESS
252139
U10968
oai:infoscience.tind.io:134804
article
GLOBAL_SET
SV
105396
GR-HE-ARTICLE-2009-002
EPFL
PUBLISHED
REVIEWED
ARTICLE