K-area, Hofer metric and geometry of conjugacy classes in Lie groups

Inventiones Mathematicae

Volumn 146, Issue 1, 2001, Pages 93-141

  Entov, Michael ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035600381     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220100161     Document Type: Article

References (55)

1. Agnihotri, S., Woodward, C., Eigenvalues of products of unitary matrices and quantum Schubert calculus, Math. Res. Lett. 5:6 (1998), 817-836
2. Akveld, M., Salamon, D., Loops of Lagrangian submanifolds and pseudoholomorphic discs, preprint, 2000. Available as math.SG/0003079
3. Bao, D., Chern, S.-S., Chen, Z., An introduction to Riemann-Finsler geometry, Springer, 2000
4. 1 \ S for S a finite set, Ph.D. thesis, Univ. of Chicago, 1999
5. Bertram, A., Quantum Schubert calculus, Adv. Math. 128:2 (1997), 289-305
6. Bertram, A., Ciocan-Fontanine, I., Fulton, W., Quantum multiplication of Schur polynomials, J. of Algebra 219:2 (1999), 728-746
7. Borel, A., Kählerian coset spaces of semisimple Lie groups, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1147-1151
8. Séminaire C. Chevalley, 1956-1958, Classification des groupes de Lie algébriques, Paris, 1958
9. Conley, C., Zehnder, E., The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Invent. math. 73 (1983), 33-49
10. Floer, A., Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), 575-611
11. Floer, A., Hofer, H., Coherent orientations for periodic orbit problems in symplectic geometry, Math. Zeit. 212 (1993), 13-38
12. Floer, A., Hofer, H., Salamon, D., Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995), 251-292
13. Fukaya, K., Ono, K., Arnold conjecture and Gromov-Witten invariant, Topology 38 (1999), 933-1048
14. Guillemin, V., Lerman, E., Sternberg, S., Symplectic fibrations and multiplicity diagrams, Cambridge University Press, 1996
15. Gromov, M., Pseudoholomorphic curves in symplectic manifolds, Invent. math. 82 (1985), 307-347
16. Gromov, M., Positive curvature, macroscopic dimension, spectral gaps and higher signatures, in: Functional Analysis of the 21st century, S. Gindikin, J. Lepowsky, R. Wilson, eds., Birkhäuser, 1996
17. Hofer, H., On the topological properties of symplectic maps, Proc. of the Royal Soc. of Edinburgh 115A (1990), 25-28
18. Hofer, H., Salamon, D., Floer homology and Novikov rings, in: The Floer Memorial Volume, H. Hofer, C. Taubes, A. Weinstein, E. Zehnder, eds., Birkhäuser, 1995
19. Hofer, H., Zehnder, E., Symplectic invariants and Hamiltonian dynamics, Birkhäuser, 1994
20. Jeffrey, L., Weitsman, J., Bohr-Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula, Comm. Math. Phys. 150:3 (1992), 593-630
21. ∞-geometry: energy and stability of flows II, Invent. math. 122 (1995), 35-69
22. Lalonde, F., McDuff, D., The geometry of symplectic energy, Ann. of Math. 141 (1995), 349-371
23. Liu, G., Tian, G., Floer homology and Arnold conjecture, J. Diff. Geom. 49 (1998), 1-74
24. Lu, G., Arnold conjecture and Piunikhin-Salamon-Schwarz's isomorphism between Floer homology and quantum homology, preprint, math.DG/0011155, 2000
25. McDuff, D., Slimowitz, J., Hofer-Zehnder capacity and length minimizing Hamiltonian paths, preprint, math.SG/0101085, 2000
26. Meinrenken, E., Woodward, C., Hamiltonian loop group actions and Verlinde factorization, J. Differential Geom. 50:3 (1998), 417-469
27. Moser, J., On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 288-294
28. Piunikhin, S., Salamon, D., Schwarz, M., Symplectic Floer-Donaldson theory and quantum cohomology, in: Contact and Symplectic Geometry, C.B. Thomas, ed., Cambridge Univ. Press, 1996
29. Polterovich, L., Symplectic displacement energy for Lagrangian submanifolds, Ergodic Th. and Dynam. Syst. 13 (1993), 357-367
30. Polterovich, L., Gromov's K-area and symplectic rigidity, Geom. and Funct. Analysis 6 (1996), 726-739
31. Polterovich, L., Hamiltonian loops and Arnold's principle, Amer. Math. Soc. Transl. (2) 180 (1997), 181-187
32. Polterovich, L., Symplectic aspects of the first eigenvalue, J. für die reine und angew. Math. 502 (1998), 1-17
33. Polterovich, L., Hofer's diameter and Lagrangian intersections, Intern. Math. Res. Notices 4 (1998), 217-223
34. Polterovich, L., The geometry of the group of symplectic diffeomorphisms (to be published) (1999)
35. Ratiu, T., Schmid, R., The Differentiable Structure of Three Remarkable Diffeomorphism Groups, Math. Zeit. 177 (1981), 81-100
36. Ruan, Y., Topological Sigma Model and Donaldson type invariants in Gromov theory, Duke Math. J. 83 (1996), 461-500
37. Ruan, Y., Tian, G., A mathematical theory of quantum cohomology, Math. Res. Lett. 1 (1994), 269-278
38. Ruan, Y., Tian, G., A mathematical theory of quantum cohomology, J. Diff. Geom. 42:2 (1995), 259-367
39. Salamon, D., Lectures on Floer homology, in: Symplectic geometry and topology (Park City, UT, 1997), 143-229, IAS/Park City Math. Ser., 7, AMS, 1999
40. Salamon, D., Zehnder, E., Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. in Pure and Appl. Math. 45 (1992), 1303-1360
41. Schwarz, M., Morse homology, Birkhäuser, 1993
42. Schwarz, M., PhD thesis, ETH-Zürich, Diss. ETH No. 11182, 1995
43. Schwarz, M., A quantum cup-length estimate for symplectic fixed points, Invent. math. 133 (1998), 353-397
44. Schwarz, M., On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193:2 (2000), 419-461
45. 1 of symplectic automorphisms groups and invertibles in quantum homology rings, Geom. and Funct. Analysis 7 (1997), 1046-1095
46. Serre, J.-P., Représentations linéaires et espaces homogènes Kählériens des groupes de Lie compacts, Sém. Bourbaki, 1953/54, Exp. 100, Paris, 1959
47. Siebert, B., Tian, G., On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator, Asian J. Math. 1:4 (1997), 679-695
48. Simpson, C.T., Products of matrices, in: Differential Geometry, Global Analysis and Topology, Canadian Math. Soc. Conf. Proc. 12, AMS (1992), 157-185
49. Siegel, C., Moser, J., Lectures on Celestial Mechanics, Springer, 1971
50. Slimowitz, J., PhD thesis, SUNY at Stony Brook, 1998
51. Teleman, C., Woodward, C., Parabolic bundles, products of conjugacy classes, and quantum cohomology, preprint, math.AG/0012241, 2000
52. Viterbo, C., Symplectic topology as the geometry of generating functions, Math. Ann., 292 (1992), 685-710
53. Wang, H.-C., Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), 1-32
54. Witten, E., Two-dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geom. 1 (1991), 243-310
55. Witten, E., The Verlinde algebra and the cohomology of the Grassmannian, in: Geometry, topology and physics, Conf. Proc. Lect. Notes Geom. Topology, IV, International Press (1995), 357-422