000171686 001__ 171686
000171686 005__ 20181203022538.0
000171686 022__ $$a0022-4049
000171686 02470 $$2ISI$$a000287911100018
000171686 0247_ $$2doi$$a10.1016/j.jpaa.2010.09.001
000171686 037__ $$aARTICLE
000171686 245__ $$aA counter-example to a conjecture of Felix
000171686 269__ $$a2011
000171686 260__ $$bElsevier$$c2011
000171686 336__ $$aJournal Articles
000171686 520__ $$aIf X is a simply connected space of finite type, then the rational homotopy groups of the based loop space of X possess the structure of a graded Lie algebra, denoted L-x. The radical of L-x, which is an important rational homotopy invariant of X, is of finite total dimension if the Lusternik-Schnirelmann category of X is finite. Let X be a simply connected space with finite Lusternik-Schnirelmann category. If dim L-x < infinity, i.e., if X is elliptic, then L-x is its own radical, and therefore the total dimension of the radical of L-x in odd degrees is less than or equal to its total dimension in even degrees (Friedlander and Halperin (1979) [8]). Felix conjectured that this inequality should hold for all simply connected spaces with finite Lusternik-Schnirelmann category. We prove Felix's conjecture in some interesting special cases, then provide a counter-example to the general case. (C) 2010 Elsevier B.V. All rights reserved.
000171686 6531_ $$aHomotopy Lie-Algebra
000171686 6531_ $$aSpaces
000171686 700__ $$aSimoncini, Fabio
000171686 773__ $$j215$$q1398-1404$$tJournal Of Pure And Applied Algebra
000171686 909C0 $$0252139$$pUPHESS$$xU10968
000171686 909CO $$ooai:infoscience.tind.io:171686$$pSV$$particle
000171686 917Z8 $$x105396
000171686 937__ $$aEPFL-ARTICLE-171686
000171686 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000171686 980__ $$aARTICLE