Skip to main content Accessibility help
×
Home

Cohomology of Bieberbach groups

  • Howard Hiller (a1)

Extract

Recently, Szczepariski [11] has constructed examples of aspherical manifolds with the ℚ-homology of a sphere. More precisely, if k is a commutative ring of characteristic zero containing , the following theorem holds.

Copyright

References

Hide All
1.Bieberbach, L.. Über die Bewegungsgruppen der Euklidischen Raume. Math. Ann., 70 (1910), 297336.
2.Bourbaki, N.. Groupes et algèbres de Lie, Chs. IV-V-VI (Hermann, Paris, 1968).
3.Charlap, L.. Compact flat Riemannian manifolds I. Ann. Math., 81 (1965), 1530.
4.Charlap, L. and Vasquez, A.. Compact flat Riemannian manifolds II: The cohomology of Z/p-manifolds. Amer. J. Math., 87 (1965), 551563.
5.Chevalley, C.. Invariants of finite groups generated by reflections. Amer. J. Math., 78 (1955), 778782.
6.Hantzsche, W. and Wendt, H.. Dreidimensionale euklidische Raumformen. Math. Ann., 110 (1934/1935), 593611.
7.Hiller, H.. Flat manifolds with Z/p2 holonomy. To appear in L'Enseignement Math.
8.Maxwell, G.. Compact Euclidean space forms. J. Algebra, 44 (1977), 191195.
9.Maxwell, G.. The crystallography of Coxeter groups. J. Algebra, 35 (1975), 159178.
10.Stanley, R.. Relative invariants of finite groups generated by pseudo-reflections. J. Algebra, 49 (1977), 134148.
11.Szczepański, A.. Aspherical manifolds with the Q-homology of a sphere. Mathematika, 30 (1983), 291294.
12.Wolf, J.. Spaces of constant curvature (McGraw-Hill, New York, 1967).
13.Yau, S.-T.. Compact flat Riemannian manifolds. J. Diff. Geom., 6 (1972), 395402.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed