Proceedings of the American Mathematical Society

Author(s): J. P. Rossetti; P. A. Tirao
Journal: Proc. Amer. Math. Soc. 124 (1996), 2491-2499.
MSC (1991): Primary 53C20; Secondary 20H15
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Abstract: In this paper we construct a family of compact flat manifolds, for all dimensions $n\ge 3$ , with holonomy group isomorphic to $\mathbf {Z}_2^2$ and first Betti number zero.

[An]: Andrews G., The Theory of Partitions (Encyclopedia of Mathematics and its Applications 2), Addison-Wesley, 1976. MR 58:27738
[Ca]: Calabi E., Closed, locally euclidean, 4-dimensional manifolds, Bull. Amer. Math. Soc. 63 (1957), 135 (abstract).
[Ch]: Charlap L., Bieberbach Groups and Flat Manifolds, Springer-Verlag, New York, 1986. MR 88j:57042
[Co]: Cobb P., Manifolds with holonomy group $\mathbf {Z} _2\oplus \mathbf {Z} _2$ and first Betti number zero, J. Differential Geometry 10 (1975), 221--224. MR 51:11343
[DM]: Dotti Miatello I. and Miatello R. J., Isospectral compact flat manifolds, Duke Mathematical Journal 68 (1992), 489--498. MR 94b:53066
[Hi]: Hiller H., Cohomology of Bieberbach groups, Mathematika 32 (1985), 55--59. MR 87h:53061
[HS]: Hiller H. and Sah C., Holonomy of flat manifolds with $\beta _1=0$ , Quart. J. Math. Oxford (2) 37 (1986), 177--187. MR 88f:53073
[Re]: Reiner I., Integral representations of cyclic groups of prime order, Proc. Amer. Math. Soc. 8 (1957), 142--146. MR 18:717a
[Wo]: Wolf J., Spaces of constant curvature, McGraw-Hill, 1967. MR 36:829

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C20, 20H15

J. P. Rossetti
Affiliation: FAMAF, Universidad Nacional de Córdoba, Argentina

Rossetti, J. P.; Tirao, P. A, Compact flat manifolds with holonomy group $Z\sb 2\oplus Z\sb 2$. II, Rend. Sem. Mat. Univ. Padova 101 (1999), 99--136. (English) MR 2000j:57075

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