Homotopy theory and circle actions on symplectic manifolds

• Autorzy: John Oprea
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 45
• Numer: 1
• Strony: 63-86

Daty

wydano

1998

Twórcy

autor

John Oprea

• Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115, U.S.A.

Bibliografia

• [ABKLR] B. Aebischer, M. Borer, M. Kalin, Ch. Leuenberger and H. M. Reimann, Symplectic Geometry, Progress in Math., vol. 124, Birkhäuser, 1994.
• [AL] M. Audin and J. Lafontaine, Holomorphic Curves in Symplectic Geometry, Progress in Math., vol. 117, Birkhäuser, 1994.
• [AM] R. Abraham and J. Marsden, Foundations of Mechanics, Addison-Wesley, 2nd ed., 1978.
• [AP] C. Allday and V. Puppe, Cohomological Methods in Transformation Groups, Cambridge Studies in Advanced Mathematics 32, Cambridge U. Press, 1993.
• [Au1] M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress in Math., vol. 93, Birkhäuser, 1991.
• [Au2] M. Audin, Exemples de variétés presque complexes, L'Enseignement Math. 37 (1991), 175-190.
• [BG] C. Benson and C. Gordon, Kähler and symplectic structures on nilmanifolds, Topology 27 (1988), 513-518.
• [Bes] A. Besse, Einstein Manifolds, Ergebnisse der Math. und ihrer Grenz. (3), vol. 10, Springer-Verlag, 1987.
• [BoHi] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, Amer. J. Math. 80 (1958), 458-538.
• [Br] G. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972.
• [BH] W. Browder and W-C. Hsiang, G-Actions and the Fundamental Group, Invent. Math. 65 (1982), 411-424.
• [DGMS] P. Deligne, P. Griffiths, J. Morgan, and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), 245-274.
• [Fr] T. Frankel, Fixed points and torsion on Kähler manifolds, Annals of Math. 70 no. 1 (1959), 1-8.
• [G1] D. Gottlieb, Applications of bundle map theory, Trans. Amer. Math. Soc. 171 (1972), 23-50.
• [G2] D. Gottlieb, The trace of an action and the degree of a map, Trans. Amer. Math. Soc. 293 (1986), 381-410.
• [G3] D. Gottlieb, Lifting actions in fibrations, Lecture Notes in Math., vol. 657, Springer-Verlag, (1977), 217-254.
• [GM] P. Griffiths and J. Morgan, Rational Homotopy Theory and Differential Forms, Birkhäuser, 1981.
• [Has] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106 (1989), 65-71.
• [Has] A. Hattori and T. Yoshida, Lifting compact group actions in fiber bundles, Japan. J. Math. 2 (1976), 13-25.
• [Kr] V. Kraines, Topology of quaternionic manifolds, Trans. Amer. Math. Soc. 122 (1966), 357-367.
• [LO1] G. Lupton and J. Oprea, Symplectic manifolds and formality, J. Pure and Appl. Algebra 91 (1994), 193-207.
• [LO2] G. Lupton and J. Oprea, z Cohomologically symplectic spaces: toral actions and the Gottlieb group, Trans. Amer. Math. Soc. 347 no. 1 (1995), 261-288.
• [Mas] W. Massey, The non-existence of almost complex structures on quaternionic projective spaces, Pac. J. Math. 12 (1962), 1379-1384.
• [Mc1] D. McDuff, Symplectic diffeomorphisms and the flux homomorphism, Invent. Math. 77 (1984), 353-366.
• [Mc2] D. McDuff, Examples of simply-connected, symplectic non-Kählerian manifolds, J. Diff. Geom. 20 (1984), 267-277.
• [Mc3] D. McDuff, The moment map for circle actions on symplectic manifolds, J. Geom. Phys. 5 no. 2 (1988), 149-160.
• [McS] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Math. Monographs, Oxford U. Press, 1995.
• [Mo] G. Mostow, Factor spaces of solvable groups, Annals of Math. 60 (1954), 1-27.
• [No] K. Nomizu, On the cohomology of homogeneous spaces of nilpotent Lie groups, Annals of Math. 59 (1954), 531-538.
• [On1] K. Ono, Equivariant projective imbedding theorem for symplectic manifolds, J. Fac. Sci. Univ. Tokyo IA Math. 35 (1988), 381-392.
• [On2] K. Ono, Obstruction to circle group actions preserving symplectic structure, Hokkaido Math. J. 21 (1992), 99-102.
• [On3] K. Ono, Some remarks on group actions in symplectic geometry, J. Fac. Sci. Univ. Tokyo 35 (1988), 431-437.
• [Sp] E. Spanier, Algebraic Topology, McGraw-Hill, 1966.
• [Su] D. Sullivan, Infinitesimal computations in topology, Publ. IHES 47 (1978), 269-331.
• [Th] W. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), 467-468.
• [Ti] D. Tischler, Closed 2-forms and an embedding theorem for symplectic manifolds, J. Diff. Geom. 12 (1977), 229-235.
• [TO] A. Tralle and J. Oprea, Symplectic manifolds with no Kähler structure, Lecture Notes in Math., vol. 1661, Springer-Verlag, 1997.
• [Wa] R. Warfield, Nilpotent Groups, Lecture Notes in Math., vol. 513, Springer-Verlag, 1976.
• [Yau] S. T. Yau, Remarks on the group of isometries of a riemannian manifold, Topology 16 (1977), 239-247.