TY - EJOUR
DO - 10.1016/j.jpaa.2010.09.001
AB - If 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.
T1 - A counter-example to a conjecture of Felix
DA - 2011
AU - Simoncini, Fabio
JF - Journal Of Pure And Applied Algebra
SP - 1398-1404
VL - 215
EP - 1398-1404
PB - Elsevier
ID - 171686
KW - Homotopy Lie-Algebra
KW - Spaces
SN - 0022-4049
ER -