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Title

Category weight: new ideas concerning Lusternik-Schnirelmann category

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Affiliations

  1. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg 1, Germany

Bibliography

  1. [A] V. I. Arnold, Mathematical Methods in Classical Mechanics, Springer, Berlin 1989.
  2. [B] A. Bassi, Su alcuni nuovi invarianti delle varietà topologiche, Annali di Math. 16 (1935), 275-297.
  3. [BG] I. Berstein and T. Ganea, The category of a map and of a cohomology class, Fund. Math. 50 (1961/2), 265-279.
  4. [CZ] C. Conley and E. Zehnder, The Birkhoff-Lewis Fixed Point Theorem and a Conjecture of V.I. Arnold, Invent. Math. 73 (1983), 33-49.
  5. [FH] E. Fadell and S. Husseini, Category weight and Steenrod operations, Boletin de la Sociedad Matemática Mexicana 37 (1992), 151-161.
  6. [F] I. Fary, Sur la catégorie des classes de homologie d'un espace, Proc. Intern. Congr. Math. 1954, 2, 215, North-Holland, Amsterdam 1957.
  7. [FeH] Y. Felix and S. Halperin, Rational L.-S. category and its applications, Trans. Amer. Math. Soc. 273 (1982), 1-38.
  8. [Fet] A. I. Fet, A connection between the topological properties and the number of extremals on a manifold (Russian), Doklady AN SSSR 88 (1953), 415-417.
  9. [Fl1] A. Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math 42 (1989), 335-356.
  10. [Fl2] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575-611.
  11. [Fox] R. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. 42 (1941), 333-370.
  12. [FE] S. Froloff and L. Elsholz, Limite inférieure pour le nombre des valeurs critiques d'une fonction, donné sur une variété, Math. Sbornik 42, 5 (1935), 637-643.
  13. [G] T. Ganea, Some problems on numerical homotopy invariants, Symposium in Algebraic Topology, Seattle 1971, 23-30, Lecture Notes in Mathematics 249, Springer, Berlin 1971.
  14. [GM] V. K. A. M. Gugenheim and J. P. May, On the Theory and Applications of Differential Torsion Products, Memoirs Amer. Math. Soc. 142, AMS, Providence, Rhode Island 1974.
  15. [H] H. Hofer, Lusternik-Schnirelmann theory for Lagrangian intersections, Annales de l'inst. Henri Poincaré- analyse non linéaire 5 (1988), 465-499.
  16. [HZ] H. Hofer and E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser, Basel 1994.
  17. [I] N. Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, preprint 1997.
  18. [J] I. M. James, On category, in the sense of Lusternik-Schnirelmann, Topology 17 (1978), 331-349.
  19. [K] D. Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431-449.
  20. [LS] L. A. Lusternik and L. G. Schnirelmann, Méthodes topologiques dans les problèmes variationnels, Hermann, Paris 1934.
  21. [MS] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Clarendon Press, Oxford 1995.
  22. [R1] Yu. B. Rudyak, On the Ganea conjecture for manifolds, Proc. Amer. Math. Soc. 125 (1997), 2511-2512.
  23. [R2] Yu. B. Rudyak, On category weight and its applications, Topology 38 (1999), 37-55.
  24. [R3] Yu. B. Rudyak, On analytical applications of stable homotopy (the Arnold conjecture, critical points), Math. Zeitschrift, to appear.
  25. [RO] Yu. B. Rudyak and J. Oprea, On the Lusternik-Schnirelmann Category of Symplectic Manifolds and the Arnold Conjecture, Math. Zeitschrift, to appear.
  26. [S1] J. Strom, Two Special Cases of Ganea's Conjecture, Trans. Amer. Math. Soc., to appear.
  27. [S2] J. Strom, Essential category weight, preprint, 1997.
  28. [S3] J. Strom, Essential category weight and classifying spaces, preprint, 1997.
  29. [Sv] A. Svarc, The genus of a fiber space, Amer. Math. Soc. Translations 55 (1966), 49-140.
  30. [Sw] R. W. Switzer, Algebraic Topology - Homotopy and Homology, Springer, Berlin 1975.
  31. [T] F. Takens, The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelmann category, Invent. Math. 6 (1968), 197-244.
  32. [To] G. Toomer, Lusternik-Schnirelmann Category and the Moore Spectral Sequence, Math. Z. 138 (1974), 123-143.
  33. [W] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. 45 (1939), 243-327.
Banach Center Publications
1998/45/1
Export to PBN, Opens in new tab
Pages:
47-61
Main language of publication
English
Published
1998
Exact and natural sciences