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1998 | 45 | 1 | 13-24
Tytuł artykułu

On Arnold's conjecture for symplectic fixed points

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
45
Numer
1
Strony
13-24
Opis fizyczny
Daty
wydano
1998
Twórcy
autor
  • Department of Mathematics, Ochanomizu University, Otsuka, Tokyo 112, Japan
Bibliografia
  • [1] M. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Phil. Soc. 77 (1975), 43-69, II, ibid. 78 (1975), 405-432.
  • [2] V. I. Arnold, Mathematical Methods in Classical Mechanics, Graduate Text in Mathematics 60, Springer Verlag.
  • [3] K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. (1997).
  • [4] M. Chaperon, Une idée du type géodesiques brisées, Comptes Rendues Paris 298 (1984), 293-296.
  • [5] Y. Chekanov, Hofer's symplectic energy and Lagrangian intersections, in: Contact and Symplectic Geometry, ed. by C. B. Thomas, Cambridge University Press, 1996; Lagrangian intersections, symplectic energy and areas of holomorphic curves, preprint.
  • [6] C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math. 73 (1983), 33-49; Morse type index theory for flows and periodic solutions for Hamiltonian systems, Comm. Pure Appl. Math. 37 (1984), 207-253.
  • [7] A. Floer, Morse theory for lagrangian intersections, Journ. Differ. Geom. 28 (1988), 513-547; The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), 775-813; A relative Morse index for the symplectic action, Comm. Pure Appl. Math. 41 (1988), 393-407; Witten's complex and infinite dimensional Morse theory, Journ. Differential Geom. 30 (1989), 207-221; Cup length estimate on lagrangian intersections, Comm. Pure Appl. Math. 42 (1989), 335-357.
  • [8] A. Floer, Holomorphic spheres and symplectic fixed points, Comm. Math. Phys. 120 (1989), 575-611.
  • [9] A. Floer and H. Hofer, Coherent orientations for periodic orbits problems in symplectic geometry, Math. Z. 212 (1993), 13-38.
  • [10] A. Floer, H. Hofer and D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. Journ. 80 (1995), 251-292.
  • [11] K. Fukaya, The symplectic S-cobordism conjecture: a summary, in: Geometry and Physics, ed. by J. E. Andersen, J. Dupont, H. Pedersen and A. Swann, Lecture Notes in Pure and Appl. Math. 184 (1997), 209-219.
  • [12] K. Fukaya and K. Ono, Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds (announcement); Arnold conjecture and Gromov-Witten invariant, preprint, 1996.
  • [13] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
  • [14] H. Hofer, Lagrangian embeddings and critical point theory, Ann. Inst. H. Poincaré, Anal. Non Linéaire 2 (1985), 407-462; Lusternik-Schnirelmann theory for Lagrangian intersections, ibid. 5 (1988), 465-499.
  • [15] H. Hofer and D. Salamon, Floer homology and Novikov rings, Floer memorial volume, ed. by H. Hofer, C. Taubes, A. Weinstein and E. Zehnder, 483-524, Birkhäuser 1995.
  • [16] M. Kontsevich, Enumeration of rational curves by torus actions, in: Moduli space of curves, ed. by H. Dijkgraaf, C. Faber, G. v. d.Geer, 335-368, Progress in Mathematics 129, Birkhäuser 1995.
  • [17] M. Kuranishi, New proof for the existence of locally free complete families of complex structures, in: Conference on Complex Analysis, 1996 Mineapolis, Springer-Verlag.
  • [18] F. Laudenbach and J.-C. Sikorav, Persistence d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent, Invent. Math. 82 (1985), 349-358.
  • [19] H. V. Lê and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, Topology 34 (1995), 155-176.
  • [20] H. V. Lê and K. Ono, Cup-length estimate for symplectic fixed points, in: Contact and Symplectic Geometry, 268-295, ed. by C. B. Thomas, Publication of the Newton Institute, Cambridge Univ. Press, 1996.
  • [21] J. Li and G. Tian, Virtual moduli cycles and Gromov-Witten invariants for general symplectic manifolds, preprint 1996.
  • [22] G. Liu and G. Tian, preprint 1996.
  • [23] D. McDuff, Elliptic methods in symplectic geometry, Bull. Amer. Math. Soc. 23 (1990), 311-358.
  • [24] D. McDuff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lecture Ser., 6, Amer. Math. Soc. 1994.
  • [25] Y. G. Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks, I, Comm. Pure Appl. Math. 46 (1993), 949-994, II ibid. 46 (1993), 995-1012, III, in: Floer Memorial Volume, Birkhäuser 1995.
  • [26] K. Ono, On the Arnold conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995), 519-537.
  • [27] S. Piunikhin, D. Salamon and M. Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, in: Contact and Symplectic Geometry, ed. by C. B. Thomas, Cambridge Univ. Press 1996.
  • [28] Y. Ruan, Virtual neighborhoods and pseudoholomorphic curves, preprint 1996.
  • [29] D. Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990), 113-140.
  • [30] D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992), 1303-1360.
  • [31] M. Schwarz, Quantum cup-length estimate for symplectic fixed points, preprint 1996.
  • [32] M. Schwarz, Morse homology, Progress in Math. 111, Birkhäuser, 1993.
  • [33] B. Siebert, Gromov-Witten invariants for general symplectic manifolds, preprint 1996.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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