Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Compact flat manifolds
with holonomy group $ \mathbf {Z}_2\oplus \mathbf {Z}_2$

Authors: J. P. Rossetti and P. A. Tirao
Journal: Proc. Amer. Math. Soc. 124 (1996), 2491-2499
MSC (1991): Primary 53C20; Secondary 20H15
MathSciNet review: 1353397
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [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

Similar Articles

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

Retrieve articles in all journals with MSC (1991): 53C20, 20H15

Additional Information

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

P. A. Tirao
Affiliation: FAMAF Universidad Nacional de Córdoba, Argentina

Keywords: Bieberbach groups. Flat manifolds
Received by editor(s): November 29, 1994
Additional Notes: Supported in part by FaMAF and CONICOR
Communicated by: Christopher Croke
Article copyright: © Copyright 1996 American Mathematical Society