Category weight: new ideas concerning Lusternik-Schnirelmann category
Banach Center Publications (1998)
- Volume: 45, Issue: 1, page 47-61
- ISSN: 0137-6934
Access Full Article
topHow to cite
topRudyak, 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- [A] V. I. Arnold, Mathematical Methods in Classical Mechanics, Springer, Berlin 1989.
- [B] A. Bassi, Su alcuni nuovi invarianti delle varietà topologiche, Annali di Math. 16 (1935), 275-297.
- [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
- [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
- [FH] E. Fadell and S. Husseini, Category weight and Steenrod operations, Boletin de la Sociedad Matemática Mexicana 37 (1992), 151-161. Zbl0848.55001
- [F] I. Fary, Sur la catégorie des classes de homologie d'un espace, Proc. Intern. Congr. Math. 1954, 2, 215, North-Holland, Amsterdam 1957.
- [FeH] Y. Felix and S. Halperin, Rational L.-S. category and its applications, Trans. Amer. Math. Soc. 273 (1982), 1-38.
- [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.
- [Fl1] A. Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math 42 (1989), 335-356. Zbl0683.58017
- [Fl2] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575-611. Zbl0755.58022
- [Fox] R. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. 42 (1941), 333-370. Zbl67.0741.02
- [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
- [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.
- [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.
- [H] H. Hofer, Lusternik-Schnirelmann theory for Lagrangian intersections, Annales de l'inst. Henri Poincaré- analyse non linéaire 5 (1988), 465-499.
- [HZ] H. Hofer and E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser, Basel 1994. Zbl0805.58003
- [I] N. Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, preprint 1997. Zbl0947.55006
- [J] I. M. James, On category, in the sense of Lusternik-Schnirelmann, Topology 17 (1978), 331-349. Zbl0408.55008
- [K] D. Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431-449. Zbl0146.19201
- [LS] L. A. Lusternik and L. G. Schnirelmann, Méthodes topologiques dans les problèmes variationnels, Hermann, Paris 1934. Zbl56.1134.02
- [MS] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Clarendon Press, Oxford 1995. Zbl0844.58029
- [R1] Yu. B. Rudyak, On the Ganea conjecture for manifolds, Proc. Amer. Math. Soc. 125 (1997), 2511-2512. Zbl0882.55003
- [R2] Yu. B. Rudyak, On category weight and its applications, Topology 38 (1999), 37-55. Zbl0927.55005
- [R3] Yu. B. Rudyak, On analytical applications of stable homotopy (the Arnold conjecture, critical points), Math. Zeitschrift, to appear.
- [RO] Yu. B. Rudyak and J. Oprea, On the Lusternik-Schnirelmann Category of Symplectic Manifolds and the Arnold Conjecture, Math. Zeitschrift, to appear.
- [S1] J. Strom, Two Special Cases of Ganea's Conjecture, Trans. Amer. Math. Soc., to appear.
- [S2] J. Strom, Essential category weight, preprint, 1997.
- [S3] J. Strom, Essential category weight and classifying spaces, preprint, 1997.
- [Sv] A. Svarc, The genus of a fiber space, Amer. Math. Soc. Translations 55 (1966), 49-140.
- [Sw] R. W. Switzer, Algebraic Topology - Homotopy and Homology, Springer, Berlin 1975. Zbl0305.55001
- [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
- [To] G. Toomer, Lusternik-Schnirelmann Category and the Moore Spectral Sequence, Math. Z. 138 (1974), 123-143. Zbl0284.55012
- [W] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. 45 (1939), 243-327. Zbl0022.40702
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.