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Felix, Yves; Halperin, Stephen; Thomas, Jean-Claude

The homotopy Lie algebra for finite complexes. (English) Zbl 0504.55005

Publ. Math., Inst. Hautes Étud. Sci. 56, 179-202 (1982).
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Cited in 3 Reviews
Cited in 16 Documents

MSC:

55P62 Rational homotopy theory
55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
55Q15 Whitehead products and generalizations
17B70 Graded Lie (super)algebras

Keywords:

simply connected CW complexes whose rational homology is finite dimensional in each degree; rational homotopy Lie algebra of a space; Lusternik-Schnirelmann category of the localization; free sub Lie algebra on two homogeneous generators

Citations:

Zbl 0101.158
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\textit{Y. Felix} et al., Publ. Math., Inst. Hautes Étud. Sci. 56, 179--202 (1982; Zbl 0504.55005)
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References:

[1] P. Andrews, M. Arkowitz, Sullivan’s minimal models and higher order Whitehead products,Can. J. Math., XXX, no 5 (1978), 961–982. · Zbl 0441.55012
[2] L. Avramov, Free Lie subalgebras of the cohomology of local rings,Trans. A.M.S.,270 (1982), 589–608. · Zbl 0516.13022
[3] L. Avramov, Differential graded models for local rings, to appear. · Zbl 0509.13010
[4] A. K. Bousfield, V. K. A. M. Gugenheim, On the P.L. de Rham theory and rational homotopy type,Memoirs A.M.S.,179 (1976). · Zbl 0338.55008
[5] H. Cartan, S. Eilenberg,Homological Algebra, Princeton University Press, no 19 (1956).
[6] Y. Felix, Modèles bifiltrés: une plaque tournante en homotopie rationnelle,Can. J. Math.,23 (no 26) (1981), 1448–1458. · Zbl 0489.55008
[7] Y. Felix, S. Halperin, Rational LS category and its applications,Trans. A.M.S.,273 (1982), 1–38. · Zbl 0508.55004
[8] Y. Felix, J. C. Thomas, Radius of convergence of Poincaré series of loop spaces,Invent. Math.,68 (1982), 257–274. · Zbl 0488.55009
[9] J. Friedlander, S. Halperin, An arithmetic characterization of the rational homotopy groups of certain spaces,Invent. Math.,53 (1979), 117–138. · Zbl 0408.55010
[10] T. Ganea, Lusternik-Schnirelmann category and cocategory,Proc. London Math. Soc.,10 (1960), 623–639. · Zbl 0101.15802
[11] T. Gulliksen, A homological characterization of local complete intersections,Compositio mathematica,23 (3) (1971), 251–255. · Zbl 0218.13028
[12] S. Halperin, Finiteness in the minimal models of Sullivan,Trans. A.M.S.,230 (1977), 173–199. · Zbl 0364.55014
[13] S. Halperin, Spaces whose rational homology and {\(\psi\)}-homotopy is finite dimensional, to appear. · Zbl 0546.55015
[14] S. Halperin, Lectures on minimal models,Publication I.R.M.A., Vol. 3, Fasc.4 (1981), third edition. · Zbl 0505.55014
[15] J.-M. Lemaire, Algèbres connexes et homologie des espaces de lacets,Springer Lecture Notes,422 (1974). · Zbl 0293.55004
[16] J.-M. Lemaire, F. Sigrist, Sur les invariants d’homotopie rationnelle liés à la LS catégorie,Comment. Math. Helvetici (56) (1981), 103–122. · Zbl 0479.55008
[17] D. Quillen, Rational homotopy theory,Ann. of Math.,90 (1969), 205–295. · Zbl 0191.53702
[18] J. E. Roos, Relations between the Poincaré-Betti series of loop spaces and of local rings,Springer Lecture Notes,740, 285–322.
[19] D. Sullivan, Infinitesimal computations in topology,Publ. Math. I.H.E.S.,47 (1978), 269–331. · Zbl 0374.57002
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