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Flat bundles with solvable holonomy. II. Obstruction theory
Author:
William M. Goldman
Journal:
Proc. Amer. Math. Soc. 83 (1981), 175-178
MSC:
Primary 55R10; Secondary 53C10
MathSciNet review:
620007
Full-text PDF Free Access
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Additional Information
Abstract: Necessary and sufficient conditions for a connected solvable Lie group  are given so that every flat principal  -bundle over a  -complex is trivial after passing to a finite covering space.
- [1]
W. Goldman, Discontinuous groups and the Euler class, Doctoral dissertation, University of California, Berkeley, 1980.
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William
M. Goldman and Morris
W. Hirsch, Flat bundles with solvable
holonomy, Proc. Amer. Math. Soc.
82 (1981), no. 3,
491–494. MR
612747 (82e:57010), http://dx.doi.org/10.1090/S0002-9939-1981-0612747-0
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Michael
Gromov, Volume and bounded cohomology, Inst. Hautes
Études Sci. Publ. Math. 56 (1982), 5–99
(1983). MR
686042 (84h:53053)
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Heinz
Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment.
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(3,316e)
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John
Milnor, On the existence of a connection with curvature zero,
Comment. Math. Helv. 32 (1958), 215–223. MR 0095518
(20 #2020)
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Dennis
Sullivan, A generalization of Milnor’s inequality concerning
affine foliations and affine manifolds, Comment. Math. Helv.
51 (1976), no. 2, 183–189. MR 0418119
(54 #6163)
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Norman
Steenrod, The Topology of Fibre Bundles, Princeton
Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J.,
1951. MR
0039258 (12,522b)
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Friedrich
Hirzebruch, Topological methods in algebraic geometry,
Classics in Mathematics, Springer-Verlag, Berlin, 1995. Translated from the
German and Appendix One by R. L. E. Schwarzenberger; With a preface to the
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Borel; Reprint of the 1978 edition. MR 1335917
(96c:57002)
- [1]
- W. Goldman, Discontinuous groups and the Euler class, Doctoral dissertation, University of California, Berkeley, 1980.
- [2]
- W. Goldman and M. Hirsch, Flat bundles with solvable holonomy, Proc. Amer. Math. Soc. (to appear). MR 612747 (82e:57010)
- [3]
- M. Gromov, Volume and bounded cohomology, Publ. Math. Inst. Haut. Études Sci. (to appear). MR 686042 (84h:53053)
- [4]
- H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment Math. Helv. 14 (1942), 257-309. MR 0006510 (3:316e)
- [5]
- J. Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958), 215-223. MR 0095518 (20:2020)
- [6]
- D. Sullivan, A generalization of Milnor's inequality concerning affine foliations and affine manifolds, Comment. Math. Helv. 51 (1976), 183-199. MR 0418119 (54:6163)
- [7]
- N. Steenrod, The topology of fibre bundles, Princeton Univ. Press, Princeton, N. J., 1951. MR 0039258 (12:522b)
- [8]
- F. Hirzebruch, Topological methods in algebraic geometry, Springer-Verlag, Berlin and New York. MR 1335917 (96c:57002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0620007-7
PII:
S 0002-9939(1981)0620007-7
Keywords:
Solvable Lie group,
flat bundle,
obstruction,
fundamental group of a surface,
finite covering space
Article copyright:
© Copyright 1981 American Mathematical Society
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