Affinely equivalent complete flat manifolds

• Autorzy: Michal Sadowski
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Compete flat manifold; affine diffeomorphism; holonomy group; Primary: 53C99; Secondary: 53C25

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 2
• Strony: 332-338

Daty

wydano

2004-04-01

online

2004-04-01

Twórcy

autor

Michal Sadowski

• University of Gdańsk

Bibliografia

• [1] L. Charlap: Bieberbach groups and flat manifolds, Springer-Verlag, New York, 1986.
• [2] T. tom Dieck: Transformation groups, de Gruyter, Berlin, 1987.
• [3] M. Sadowski: Topological structure of complete flat manifolds with cyclic holonomy groups, to appear.
• [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
• [5] J. Wolf: Spaces of constant curvature, McGraw-Hill, 1967.

Identyfikatory

DOI

10.2478/BF02476546