Topological and affine classification of complete noncompact flat 4-manifolds

In this paper we give topological and affine classification of complete noncompact flat 4-manifolds. In particular, we show that the number of diffeomorphism classes of them is equal to 44. The affine classification uses the results of [M. Sadowski, Affinely equivalent complete flat manifolds, Cent....

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Bibliographic Details
Published in:Journal of geometry and physics 2008-11, Vol.58 (11), p.1530-1539
Main Author: Sadowski, Michał
Format: Article
Language:English
Subjects:
Bieberbach group
Complete flat 4-manifold
Holonomy group
Topological and affine classification
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Summary:In this paper we give topological and affine classification of complete noncompact flat 4-manifolds. In particular, we show that the number of diffeomorphism classes of them is equal to 44. The affine classification uses the results of [M. Sadowski, Affinely equivalent complete flat manifolds, Cent. Eur. J. Math. 2 (2) (2004) 332–338]. The affine and the topological equivalence classes are the same for flat manifolds not homotopy equivalent to S 1 , T 2 or the Klein bottle.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2008.07.003