Homotopy theory and circle actions on symplectic manifolds

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1. [ABKLR] B. Aebischer, M. Borer, M. Kalin, Ch. Leuenberger and H. M. Reimann, Symplectic Geometry, Progress in Math., vol. 124, Birkhäuser, 1994. 
2. [AL] M. Audin and J. Lafontaine, Holomorphic Curves in Symplectic Geometry, Progress in Math., vol. 117, Birkhäuser, 1994. Zbl0802.53001
3. [AM] R. Abraham and J. Marsden, Foundations of Mechanics, Addison-Wesley, 2nd ed., 1978. 
4. [AP] C. Allday and V. Puppe, Cohomological Methods in Transformation Groups, Cambridge Studies in Advanced Mathematics 32, Cambridge U. Press, 1993. Zbl0799.55001
5. [Au1] M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress in Math., vol. 93, Birkhäuser, 1991. 
6. [Au2] M. Audin, Exemples de variétés presque complexes, L'Enseignement Math. 37 (1991), 175-190. 
7. [BG] C. Benson and C. Gordon, Kähler and symplectic structures on nilmanifolds, Topology 27 (1988), 513-518. Zbl0672.53036
8. [Bes] A. Besse, Einstein Manifolds, Ergebnisse der Math. und ihrer Grenz. (3), vol. 10, Springer-Verlag, 1987. 
9. [BoHi] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, Amer. J. Math. 80 (1958), 458-538. Zbl0097.36401
10. [Br] G. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972. Zbl0246.57017
11. [BH] W. Browder and W-C. Hsiang, G-Actions and the Fundamental Group, Invent. Math. 65 (1982), 411-424. Zbl0519.57034
12. [DGMS] P. Deligne, P. Griffiths, J. Morgan, and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), 245-274. Zbl0312.55011
13. [Fr] T. Frankel, Fixed points and torsion on Kähler manifolds, Annals of Math. 70 no. 1 (1959), 1-8. Zbl0088.38002
14. [G1] D. Gottlieb, Applications of bundle map theory, Trans. Amer. Math. Soc. 171 (1972), 23-50. Zbl0251.55018
15. [G2] D. Gottlieb, The trace of an action and the degree of a map, Trans. Amer. Math. Soc. 293 (1986), 381-410. Zbl0593.57017
16. [G3] D. Gottlieb, Lifting actions in fibrations, Lecture Notes in Math., vol. 657, Springer-Verlag, (1977), 217-254. 
17. [GM] P. Griffiths and J. Morgan, Rational Homotopy Theory and Differential Forms, Birkhäuser, 1981. 
18. [Has] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106 (1989), 65-71. 
19. [Has] A. Hattori and T. Yoshida, Lifting compact group actions in fiber bundles, Japan. J. Math. 2 (1976), 13-25. Zbl0346.57014
20. [Kr] V. Kraines, Topology of quaternionic manifolds, Trans. Amer. Math. Soc. 122 (1966), 357-367. Zbl0148.16101
21. [LO1] G. Lupton and J. Oprea, Symplectic manifolds and formality, J. Pure and Appl. Algebra 91 (1994), 193-207. Zbl0789.55010
22. [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. Zbl0836.57019
23. [Mas] W. Massey, The non-existence of almost complex structures on quaternionic projective spaces, Pac. J. Math. 12 (1962), 1379-1384. Zbl0112.14702
24. [Mc1] D. McDuff, Symplectic diffeomorphisms and the flux homomorphism, Invent. Math. 77 (1984), 353-366. Zbl0538.53041
25. [Mc2] D. McDuff, Examples of simply-connected, symplectic non-Kählerian manifolds, J. Diff. Geom. 20 (1984), 267-277. Zbl0567.53031
26. [Mc3] D. McDuff, The moment map for circle actions on symplectic manifolds, J. Geom. Phys. 5 no. 2 (1988), 149-160. Zbl0696.53023
27. [McS] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Math. Monographs, Oxford U. Press, 1995. Zbl0844.58029
28. [Mo] G. Mostow, Factor spaces of solvable groups, Annals of Math. 60 (1954), 1-27. Zbl0057.26103
29. [No] K. Nomizu, On the cohomology of homogeneous spaces of nilpotent Lie groups, Annals of Math. 59 (1954), 531-538. Zbl0058.02202
30. [On1] K. Ono, Equivariant projective imbedding theorem for symplectic manifolds, J. Fac. Sci. Univ. Tokyo IA Math. 35 (1988), 381-392. Zbl0655.53027
31. [On2] K. Ono, Obstruction to circle group actions preserving symplectic structure, Hokkaido Math. J. 21 (1992), 99-102. Zbl0749.53020
32. [On3] K. Ono, Some remarks on group actions in symplectic geometry, J. Fac. Sci. Univ. Tokyo 35 (1988), 431-437. Zbl0711.53025
33. [Sp] E. Spanier, Algebraic Topology, McGraw-Hill, 1966. 
34. [Su] D. Sullivan, Infinitesimal computations in topology, Publ. IHES 47 (1978), 269-331. Zbl0374.57002
35. [Th] W. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), 467-468. Zbl0324.53031
36. [Ti] D. Tischler, Closed 2-forms and an embedding theorem for symplectic manifolds, J. Diff. Geom. 12 (1977), 229-235. Zbl0386.58001
37. [TO] A. Tralle and J. Oprea, Symplectic manifolds with no Kähler structure, Lecture Notes in Math., vol. 1661, Springer-Verlag, 1997. Zbl0891.53001
38. [Wa] R. Warfield, Nilpotent Groups, Lecture Notes in Math., vol. 513, Springer-Verlag, 1976. 
39. [Yau] S. T. Yau, Remarks on the group of isometries of a riemannian manifold, Topology 16 (1977), 239-247. Zbl0372.53020