Compact flat manifolds with holonomy group Z2⊕Z2 (II)

J. P. Rossetti; P. A. Tirao

Compact flat manifolds with holonomy group Z₂⊕Z₂ (II)

J. P. Rossetti, P. A. Tirao

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we give a complete classification of compact flat manifolds with holonomy group Z₂⊕ Z₂, with the property that the holonomy representation decomposes as a direct sum of indecomposable representations of Z-rank equal to 1 or 2. We exhibit explicit realizations of all the manifolds classified, computing the first integral homology groups. Finally, we compare the results obtained with the known results in low dimensions.

Original language	English
Pages (from-to)	99-136
Number of pages	38
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	101
State	Published - 1999
Externally published	Yes

Cite this

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abstract = "In this paper we give a complete classification of compact flat manifolds with holonomy group Z2⊕ Z2, with the property that the holonomy representation decomposes as a direct sum of indecomposable representations of Z-rank equal to 1 or 2. We exhibit explicit realizations of all the manifolds classified, computing the first integral homology groups. Finally, we compare the results obtained with the known results in low dimensions.",

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AU - Rossetti, J. P.

AU - Tirao, P. A.

PY - 1999

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N2 - In this paper we give a complete classification of compact flat manifolds with holonomy group Z2⊕ Z2, with the property that the holonomy representation decomposes as a direct sum of indecomposable representations of Z-rank equal to 1 or 2. We exhibit explicit realizations of all the manifolds classified, computing the first integral homology groups. Finally, we compare the results obtained with the known results in low dimensions.

AB - In this paper we give a complete classification of compact flat manifolds with holonomy group Z2⊕ Z2, with the property that the holonomy representation decomposes as a direct sum of indecomposable representations of Z-rank equal to 1 or 2. We exhibit explicit realizations of all the manifolds classified, computing the first integral homology groups. Finally, we compare the results obtained with the known results in low dimensions.

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M3 - 文章

AN - SCOPUS:84938579771

SN - 0041-8994

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EP - 136

JO - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

JF - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

ER -

Compact flat manifolds with holonomy group Z₂⊕Z₂ (II)

Abstract

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