Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology

Transactions of the American Mathematical Society

Volumn 352, Issue 12, 2000, Pages 5405-5433

  Cordero, Luis A ^a,d   Fernández, Marisa ^b   Gray, Alfred ^c   Ugarte, Luis ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^c Bldg 142   (United States)

^d UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044522094     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02486-7     Document Type: Article

References (32)

1. A] M.F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181-207. MR 19:172c
2. AFGM] L.C. de Andrés, M. Fernández, A. Gray, J.J. Mencía, Compact manifolds with indefinite Kahler metrics, Proc. VIth Int. Coll. Differential Geometry (Ed. L.A. Cordero), Santiago (Spain) 1988, Cursos y Congresos Univ. Santiago de Compostela (Spain) 61 (1989), 25-50. MR 91e:53066
3. AGS] E. Abbena, S. Garbiero, S. Salamon, Hermitian geometry on the Iwasawa manifold, Boll. U.M.I. B (7) 11, no. 2, suppl. (1997), 231-249. MR 98e:53121
4. BG] C. Benson, C. Gordon, Kähler and symplectic structures on nilmanifolds, Topology 27 (1988), 513-518. MR 90b:53042
5. Co] L.A. Cordero, Holomorphic principal torus bundles, curvature and compact complex nilmanifolds, Proc. Workshop on Curvature and Geometry (Ed. C.T.J. Dodson), Lancaster Univ. (U.K.) January 1989 (1989), 107-149. MR 92b:53111
6. CFG1] L.A. Cordero, M. Fernândez, A. Gray, Symplectic manifolds with no Kähler structure, Topology 25 (1986), 375-380. MR 87j:53051
7. CFG2] L.A. Cordero, M.. Fernández, A. Gray, Compact symplectic manifolds not admitting positive definite Kahler metrics, to appear, Proc. Int. Conf. on Topology and its Appl., Baku 3-9 October 1987, U.R.S.S..
8. CFG3] L.A. Cordero, M. Fernández, A. Gray, The Frölicher spectral sequence and complex compact nilmanifolds, C. R. Acad. Sei. Paris Sér. I Math. 305 (1987), 753-756. MR 89c:32081
9. CFG4] L.A. Cordero, M. Fernández, A. Gray, The Frölicher spectral sequence for compact nilmanifolds, Illinois J. Math. 35 (1991), 56-67. MR 92b:53112
10. CFG5] L.A. Cordero, M. Fernández, A. Gray, The de Rham cohomology ring of a compact nilmanifold, preprint.
11. CFGU] L.A. Cordero, M. Fernández, A. Gray, L. Ugarte, A general description of the terms in the Frölicher spectral sequence, Diff. Geom. and its Applic. 7 (1997), 75-84. MR 98m:53092
12. DGMS] P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), 245-274. MR 52:3584
13. FG] M. Fernández, A. Gray, The Iwasawa manifold, (Differential Geometry, Pemscola, 1985), Lect. Notes in Math. 1209 (1986), 157-159. MR 87k:53162
14. F] A. Frölicher, Relations between the cohomology groups of Dolbeault and topological invariants, Proc. Nat. Acad. Sei. U.S.A. 41 (1955), 641-644. MR 17:409a
15. GM] P. Griffiths, J. Morgan, Rational Homotopy Theory and Differential Forms, Progress in Math. 16, Birkhäuser, 1981. MR 82m:35014
16. Ha] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106 (1989), 65-71. MR 89i:32015
17. Hi] F. Hirzebruch, Topological Methods in Algebraic Geometry, third enlarged ed., Springer-Verlag, New York, 1966. MR 34:2573
18. KN] S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, I, II, Interscience Publ., New York, 1963, 1969. MR 27:2945; MR 38:6501
19. Ko] K. Kodaira, On the structure of compact complex analytic surfaces, I, Amer. J. Math. 86 (1964), 751-798. MR 32:4708
20. Ks] J.L. Koszul, Lectures on Fibre Bundles and Differential Geometry, Tata Inst., Bombay 1960. (Reissued Springer 1986.). MR 42:3698; MR 88e:53040
21. Ma] I.A. Mal'cev, A class of homogeneous spaces, Amer. Math. Soc. Transi. 39 (1951). MR 10:50701; MR 12:589a
22. McC] J. McCleary, User's Guide to Spectral Sequences, Publish or Perish, 1985. MR 87f:55014
23. Mu] S. Murakami, Sur certain espaces fibres principaux holomorphes dont le groupe est abélien connexe, Osaka Math. J. 13 (1961), 143-167. MR 26:788
24. Na] I. Nakamura, Complex parallelisable manifolds and their small deformations, J. Differential Geometry 10 (1975), 85-112. MR 52:14389
25. NT] J. Neisendorfer, L. Taylor, Dolbeault Homotopy Theory, Trans. Amer. Math. Soc. 245 '(1978), 183-210. MR 80f:32004
26. No] K. Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. 59 (1954), 531-538. MR 16:218c
27. R] M.S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, Berlin, 1972. MR 58:22394a
28. Sa] Y. Sakane, On compact complex parallelisable solvmanifolds, Osaka J. Math. 13 (1976), 187-212. MR 54:10692
29. Th] W.P. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), 467-468. MR 53:6578
30. Tr] A. Tralle, Applications of rational homotopy to geometry (results, problems, conjectures), Expo. Math. 14 (1996), 425-472. MR 97k:55015
31. Va] V.S. Varadarajan, Lie Groups, Lie Algebras, and their Representations, Graduate Texts in Math. 102, Springer-Verlag, Berlin, 1984. MR 85e:22001
32. Wa] H.C. Wang, Complex parallelisable manifolds, Proc. Amer. Math. Soc. 5 (1954), 771-776. MR 17:531a