There is just one rational cone-length

Cornea, Octavian

doi:10.1090/S0002-9947-1994-1260200-X

There is just one rational cone-length
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Trans. Amer. Math. Soc. 344 (1994), 835-848 Request permission

Abstract:

We show that the homotopic nilpotency of the algebra of piecewise polynomial forms on a simply-connected, finite type, CW-complex coincides with the strong L.S. category of the rationalization of that space. This is used to prove that, in the rational, simply-connected context all reasonable notions of cone-length agree. Both these two results are obtained as parts of a more general and functorial picture.

References

Mónica Clapp and Dieter Puppe, Invariants of the Lusternik-Schnirelmann type and the topology of critical sets, Trans. Amer. Math. Soc. 298 (1986), no. 2, 603–620. MR 860382, DOI 10.1090/S0002-9947-1986-0860382-0
Octavian Cornea, Cone-length and Lusternik-Schnirelmann category, Topology 33 (1994), no. 1, 95–111. MR 1259517, DOI 10.1016/0040-9383(94)90037-X

La dichotomie elliptique-hyperbolique en homotopie rationnelle

Yves Félix and Stephen Halperin, Rational LS category and its applications, Trans. Amer. Math. Soc. 273 (1982), no. 1, 1–38. MR 664027, DOI 10.1090/S0002-9947-1982-0664027-0
Yves Félix and Jean-Claude Thomas, Sur la structure des espaces de LS catégorie deux, Illinois J. Math. 30 (1986), no. 4, 574–593 (French). MR 857212
T. Ganea, Lusternik-Schnirelmann category and strong category, Illinois J. Math. 11 (1967), 417–427. MR 229240
S. Halperin, Lectures on minimal models, Mém. Soc. Math. France (N.S.) 9-10 (1983), 261. MR 736299
Jean-Michel Lemaire and François Sigrist, Sur les invariants d’homotopie rationnelle liés à la L. S. catégorie, Comment. Math. Helv. 56 (1981), no. 1, 103–122 (French). MR 615618, DOI 10.1007/BF02566201

Méthodes topologiques dans les problèmes variationnels

Daniel Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295. MR 258031, DOI 10.2307/1970725
Floris Takens, The Lusternik-Schnirelman categories of a product space, Compositio Math. 22 (1970), 175–180. MR 290365
Daniel Tanré, Homotopie rationnelle: modèles de Chen, Quillen, Sullivan, Lecture Notes in Mathematics, vol. 1025, Springer-Verlag, Berlin, 1983 (French). MR 764769, DOI 10.1007/BFb0071482