Affinely equivalent complete flat manifolds

Michal Sadowski

Open Mathematics (2004)

  • Volume: 2, Issue: 2, page 332-338
  • ISSN: 2391-5455

Abstract

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Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).

How to cite

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Michal Sadowski. "Affinely equivalent complete flat manifolds." Open Mathematics 2.2 (2004): 332-338. <http://eudml.org/doc/268815>.

@article{MichalSadowski2004,
abstract = {Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).},
author = {Michal Sadowski},
journal = {Open Mathematics},
keywords = {Primary: 53C99; Secondary: 53C25},
language = {eng},
number = {2},
pages = {332-338},
title = {Affinely equivalent complete flat manifolds},
url = {http://eudml.org/doc/268815},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Michal Sadowski
TI - Affinely equivalent complete flat manifolds
JO - Open Mathematics
PY - 2004
VL - 2
IS - 2
SP - 332
EP - 338
AB - Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).
LA - eng
KW - Primary: 53C99; Secondary: 53C25
UR - http://eudml.org/doc/268815
ER -

References

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  1. [1] L. Charlap: Bieberbach groups and flat manifolds, Springer-Verlag, New York, 1986. Zbl0608.53001
  2. [2] T. tom Dieck: Transformation groups, de Gruyter, Berlin, 1987. 
  3. [3] M. Sadowski: Topological structure of complete flat manifolds with cyclic holonomy groups, to appear. 
  4. [4] A. Szczepański: Aspherical manifolds with ℚ-homology of a sphere, Mathematika, Vol. 30, (1983), pp. 291–294. http://dx.doi.org/10.1112/S0025579300010561 Zbl0521.57019
  5. [5] J. Wolf: Spaces of constant curvature, McGraw-Hill, 1967. Zbl0162.53304

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