Category weight: new ideas concerning Lusternik-Schnirelmann category

Yuli Rudyak

Banach Center Publications (1998)

  • Volume: 45, Issue: 1, page 47-61
  • ISSN: 0137-6934

How to cite

top

Rudyak, Yuli. "Category weight: new ideas concerning Lusternik-Schnirelmann category." Banach Center Publications 45.1 (1998): 47-61. <http://eudml.org/doc/208909>.

@article{Rudyak1998,
author = {Rudyak, Yuli},
journal = {Banach Center Publications},
keywords = {Lyusternik-Shnirel'man category; symplectic manifold; Ganea conjecture},
language = {eng},
number = {1},
pages = {47-61},
title = {Category weight: new ideas concerning Lusternik-Schnirelmann category},
url = {http://eudml.org/doc/208909},
volume = {45},
year = {1998},
}

TY - JOUR
AU - Rudyak, Yuli
TI - Category weight: new ideas concerning Lusternik-Schnirelmann category
JO - Banach Center Publications
PY - 1998
VL - 45
IS - 1
SP - 47
EP - 61
LA - eng
KW - Lyusternik-Shnirel'man category; symplectic manifold; Ganea conjecture
UR - http://eudml.org/doc/208909
ER -

References

top
  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. Zbl0192.29302
  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. Zbl0516.58017
  5. [FH] E. Fadell and S. Husseini, Category weight and Steenrod operations, Boletin de la Sociedad Matemática Mexicana 37 (1992), 151-161. Zbl0848.55001
  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. Zbl0683.58017
  10. [Fl2] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575-611. Zbl0755.58022
  11. [Fox] R. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. 42 (1941), 333-370. Zbl67.0741.02
  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. Zbl61.0554.02
  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. Zbl0805.58003
  17. [I] N. Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, preprint 1997. Zbl0947.55006
  18. [J] I. M. James, On category, in the sense of Lusternik-Schnirelmann, Topology 17 (1978), 331-349. Zbl0408.55008
  19. [K] D. Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431-449. Zbl0146.19201
  20. [LS] L. A. Lusternik and L. G. Schnirelmann, Méthodes topologiques dans les problèmes variationnels, Hermann, Paris 1934. Zbl56.1134.02
  21. [MS] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Clarendon Press, Oxford 1995. Zbl0844.58029
  22. [R1] Yu. B. Rudyak, On the Ganea conjecture for manifolds, Proc. Amer. Math. Soc. 125 (1997), 2511-2512. Zbl0882.55003
  23. [R2] Yu. B. Rudyak, On category weight and its applications, Topology 38 (1999), 37-55. Zbl0927.55005
  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. Zbl0305.55001
  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. Zbl0198.56603
  32. [To] G. Toomer, Lusternik-Schnirelmann Category and the Moore Spectral Sequence, Math. Z. 138 (1974), 123-143. Zbl0284.55012
  33. [W] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. 45 (1939), 243-327. Zbl0022.40702

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.