171686
20181203022538.0
0022-4049
10.1016/j.jpaa.2010.09.001
doi
000287911100018
ISI
ARTICLE
A counter-example to a conjecture of Felix
2011
Elsevier
2011
Journal Articles
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.
Homotopy Lie-Algebra
Spaces
Simoncini, Fabio
1398-1404
Journal Of Pure And Applied Algebra
215
UPHESS
252139
U10968
oai:infoscience.tind.io:171686
article
SV
105396
EPFL-ARTICLE-171686
EPFL
PUBLISHED
REVIEWED
ARTICLE