000134804 001__ 134804
000134804 005__ 20190525071226.0
000134804 02470 $$2ISI$$a000276643400035
000134804 02470 $$a0903.1651$$2ArXiv
000134804 037__ $$aARTICLE
000134804 245__ $$aThe loop group and the cobar construction
000134804 269__ $$a2010
000134804 260__ $$c2010
000134804 336__ $$aJournal Articles
000134804 520__ $$aWe 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.
000134804 6531_ $$aLoop space
000134804 6531_ $$acobar construction
000134804 6531_ $$astrong deformation retract
000134804 6531_ $$aacyclic models
000134804 6531_ $$aDifferential Homological Algebra
000134804 6531_ $$aPerturbation-Theory
000134804 700__ $$0240499$$g105396$$aHess, Kathryn
000134804 700__ $$aTonks, Andrew
000134804 773__ $$j138$$tProceedings of the American Mathematical Society$$k5$$q1861-1876
000134804 8564_ $$uhttps://infoscience.epfl.ch/record/134804/files/proc10238.pdf$$zPostprint$$s247711$$yPostprint
000134804 909C0 $$xU10968$$0252139$$pUPHESS
000134804 909CO $$ooai:infoscience.tind.io:134804$$qGLOBAL_SET$$pSV$$particle
000134804 917Z8 $$x105396
000134804 937__ $$aGR-HE-ARTICLE-2009-002
000134804 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000134804 980__ $$aARTICLE