Contributions of rational homotopy theory to global problems in geometry
Publications Mathématiques de l'IHÉS, Volume 56 (1982), pp. 171-177.
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     author = {Grove, Karsten and Halperin, Stephen},
     title = {Contributions of rational homotopy theory to global problems in geometry},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {171--177},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {56},
     year = {1982},
     zbl = {0508.55013},
     mrnumber = {84b:58030},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1982__56__171_0/}
}
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Grove, Karsten; Halperin, Stephen. Contributions of rational homotopy theory to global problems in geometry. Publications Mathématiques de l'IHÉS, Volume 56 (1982), pp. 171-177. http://www.numdam.org/item/PMIHES_1982__56__171_0/

[1] I. K. Babenko, On analytic properties of the Poincaré series of loop spaces, Math. Zametki, 27 (1980), 751-765. | MR | Zbl

[2] J. Barge, Structures différentiables sur les types d'homotopie rationnelle simplement connexes, Ann. Scient. Éc. Norm. Sup., 9 (1976), 469-501. | Numdam | MR | Zbl

[3] M. Berger, R. Bott, Sur les variétés à courbure strictement positive, Topology, 1 (1962), 301-311. | MR | Zbl

[4] Y. Felix, S. Halperin, Rational Lusternik-Schnirelmann category and its applications, Trans. Amer. Math. Soc., 273 (1982), 1-37. | MR | Zbl

[5] Y. Felix, S. Halperin, J. C. Thomas, The homotopy Lie algebra for finite complexes, Publ. Math. I.H.E.S., ce volume, 179-202. | Numdam | MR | Zbl

[6] Y. Felix, J. C. Thomas, The radius of convergence of Poincaré series of loop spaces, Invent. math., 68 (1982), 257-274. | MR | Zbl

[7] J. B. Friedlander, S. Halperin, Rational homotopy groups of certain spaces, Invent. math., 53 (1979), 117-133. | MR | Zbl

[8] M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv., 56 (1981), 179-195. | MR | Zbl

[9] K. Grove, Condition (C) for the energy integral on certain path-spaces and applications to the theory of geodesics, J. Differential Geometry, 8 (1973), 207-223. | MR | Zbl

[10] K. Grove, Isometry-invariant Geodesics, Topology, 13 (1974), 281-292. | MR | Zbl

[11] K. Grove, S. Halperin, M. Vigué-Poirrier, The rational homotopy theory of certain path-spaces with applications to geodesics, Acta math., 140 (1978), 277-303. | MR | Zbl

[12] K. Grove, M. Tanaka, On the number of invariant closed geodesics, Acta math., 140 (1978), 33-48. | MR | Zbl

[13] S. Halperin, Finiteness in the minimal model of Sullivan, Trans. Amer. Math. Soc., 230 (1977), 173-199. | MR | Zbl

[14] S. Halperin, Spaces whose rational homotopy and ψ-homotopy are both finite dimensional, to appear. | Zbl

[15] H. Hernández-Andrade, A class of compact manifolds with positive Ricci curvature, Proc. symp. pure math. A.M.S., XXVII (1975), 73-87. | MR | Zbl

[16] J. Milnor, Singular points of complex hypersurfaces, Annals of math. studies, 61 (1968), Princeton. | MR | Zbl

[17] S. B. Myers, N. Steenrod, The group of isometries of a Riemannian manifold, Ann. of Math., 40 (1939), 400-416. | JFM | Zbl

[18] D. Quillen, Rational homotopy theory, Ann. of Math., 90 (1969), 205-295. | MR | Zbl

[19] D. Sullivan, Infinitesimal computations in topology, Publ. Math. I.H.E.S., 47 (1978), 269-331. | Numdam | MR | Zbl

[20] M. Tanaka, On the existence of infinitely many isometry-invariant geodesics, J. Differential Geometry, 17 (1982), 171-184. | MR | Zbl