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Coeffective cohomology of symplectic aspherical manifolds
Author:
Hisashi Kasuya
Journal:
Proc. Amer. Math. Soc. 140 (2012), 2835-2842
MSC (2010):
Primary 53D05
Posted:
November 29, 2011
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Abstract: We prove a generalization of the theorem which has been proved by Fernandez, Ibanez, and de Leon. By this result, we give examples of non-Kähler manifolds which satisfy the property of compact Kähler manifolds concerning the coeffective cohomology.
References
- 1.
Donu
Arapura and Madhav
Nori, Solvable fundamental groups of algebraic varieties and
Kähler manifolds, Compositio Math. 116 (1999),
no. 2, 173–188. MR 1686777
(2000k:14018), http://dx.doi.org/10.1023/A:1000879906578
- 2.
Oliver
Baues, Infra-solvmanifolds and rigidity of subgroups in solvable
linear algebraic groups, Topology 43 (2004),
no. 4, 903–924. MR 2061212
(2005c:57048), http://dx.doi.org/10.1016/S0040-9383(03)00083-1
- 3.
Armand
Borel, Linear algebraic groups, 2nd ed., Graduate Texts in
Mathematics, vol. 126, Springer-Verlag, New York, 1991. MR 1102012
(92d:20001)
- 4.
Thierry
Bouche, La cohomologie coeffective d’une
variété symplectique, Bull. Sci. Math.
114 (1990), no. 2, 115–122 (French, with
English summary). MR 1056157
(91i:58005)
- 5.
Marisa
Fernández, Raúl
Ibáñez, and Manuel
de León, A Nomizu’s theorem for the coeffective
cohomology, Math. Z. 226 (1997), no. 1,
11–23. MR
1472138 (98k:58008), http://dx.doi.org/10.1007/PL00004327
- 6.
Marisa
Fernández, Raúl
Ibáñez, and Manuel
de León, Coeffective and de Rham cohomologies of symplectic
manifolds, J. Geom. Phys. 27 (1998), no. 3-4,
281–296. MR 1645044
(99k:53053), http://dx.doi.org/10.1016/S0393-0440(97)00084-3
- 7.
Keizo
Hasegawa, A note on compact solvmanifolds with Kähler
structures, Osaka J. Math. 43 (2006), no. 1,
131–135. MR 2222405
(2007h:32035)
- 8.
Akio
Hattori, Spectral sequence in the de Rham cohomology of fibre
bundles, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1960),
289–331 (1960). MR 0124918
(23 #A2226)
- 9.
H. Kasuya, Formality and hard Lefschetz properties of aspherical manifolds. http://arxiv.
org/abs/0910.1175. To appear in Osaka J. Math.
- 10.
H. Kasuya Cohomologically symplectic solvmanifolds are symplectic. J. Symplectic Geom. 9 (2011), no. 4.
- 11.
Paulette
Libermann and Charles-Michel
Marle, Symplectic geometry and analytical mechanics,
Mathematics and its Applications, vol. 35, D. Reidel Publishing Co.,
Dordrecht, 1987. Translated from the French by Bertram Eugene Schwarzbach.
MR 882548
(88c:58016)
- 12.
G.
D. Mostow, On the fundamental group of a homogeneous space,
Ann. of Math. (2) 66 (1957), 249–255. MR 0088675
(19,561c)
- 13.
Iku
Nakamura, Complex parallelisable manifolds and their small
deformations, J. Differential Geometry 10 (1975),
85–112. MR
0393580 (52 #14389)
- 14.
Katsumi
Nomizu, On the cohomology of compact homogeneous spaces of
nilpotent Lie groups, Ann. of Math. (2) 59 (1954),
531–538. MR 0064057
(16,219c)
- 15.
M.
S. Raghunathan, Discrete subgroups of Lie groups,
Springer-Verlag, New York, 1972. Ergebnisse der Mathematik und ihrer
Grenzgebiete, Band 68. MR 0507234
(58 #22394a)
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Additional Information
Hisashi Kasuya
Affiliation:
Graduate School of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email:
khsc@ms.u-tokyo.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11421-7
PII:
S 0002-9939(2011)11421-7
Keywords:
Symplectic manifold,
solvmanifold,
polycyclic group,
coeffective cohomology
Received by editor(s):
March 3, 2011
Posted:
November 29, 2011
Communicated by:
Lei Ni
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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