RT Journal Article T1 Arnold’s conjecture and symplectic reduction A1 Ibort, A. A1 Martínez Ontalba, Celia AB Fortune (1985) proved Arnold's conjecture for complex projective spaces, by exploiting the fact that CPn-1 is a symplectic quotient of C-n. In this paper, we show that Fortune's approach is universal in the sense that it is possible to translate Arnold's conjecture on any closed symplectic manifold (Q,Omega) to a critical point problem with symmetry on loops in R(2n) With its Standard symplectic structure. PB Elsevier SN 0393-0440 YR 1996 FD 1996 LK https://hdl.handle.net/20.500.14352/57636 UL https://hdl.handle.net/20.500.14352/57636 LA eng NO V.I. Arnold, Commentary on “On a geometrical theorem”, in: Collected Works, Vol. II, ed. H. Poincare (Nauka, Moscow, MR 52 # 5337,1972) pp. 987-989.V.I. Arnold, Fixed points of symplectic diffeomorphisms, in: Mathematical Developments Arisingfrom the Hilbert Problems, Proc. Symp. Pure Math., Amer. Math. Sot. 28 (1976) 66.A. Fleer, Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989) 575-611.B. Fortune, A symplectic fixed point theorem for CP”, Inv. Math. 81 (1985) 29-46.B. Fortune and A. Weinstein, A symplectic fixed point theorem for complex projective spaces, Bull.Amer. Math. Sot. 12 (1985) 128-130.A.B. Givental, A symplectic fixed point theorem for toric manifolds, Progress in Math. Fleer Memorial Volume, 1994, to appear. M.J. Gotay and G.M. Tuynman, R2” is a universal symplectic manifold for reduction, Lett. Math. Phys. 18 (1989) 55-59.L& Hong Van and K. Ono, Symplectic fixed points, the Calabi invariant and Novikov homology,Topology 34 (1995) 155-176.H. Hofer and D. Salamon, Fleer homology and Novikov rings, preprint (1992).A. Ibort and C. Martinez Ontalba, A universal setting for Arnold’s conjecture, C. R. Acad. Sci. Paris t.318, Strie II (1994) 561-566.M. Kummer, On the construction of the reduced phase space of a hamiltonian system with symmetry,Indiana Univ. Math. J 30 (1981) 281-291.Y.-G. Oh, A symplectic fixed point theorem on R*” x Cpk, Math. Z. 203 (1990) 535-552.K. Ono, On the Arnold conjecture for weakly monotone symplectic manifolds, Inv. Math. I 19 (1995)519-537.A. Weinstein, A universal phase space for particles in Yang-Mills fields, Lett. Math. Phys. 2 (1978)417-420. NO CICYT DS Docta Complutense RD 27 abr 2024