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The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5. / Chelnokov, Grigory; Mednykh, Alexander.
в: Journal of Algebra, Том 560, 15.10.2020, стр. 48-66.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5
AU - Chelnokov, Grigory
AU - Mednykh, Alexander
PY - 2020/10/15
Y1 - 2020/10/15
N2 - There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of n-fold coverings over the orientable Euclidean manifolds G3 and G5, and calculate the numbers of non-equivalent coverings of each type. The manifolds G3 and G5 are uniquely determined among other forms by their homology groups H1(G3)=Z3×Z and H1(G5)=Z. We classify subgroups in the fundamental groups π1(G3) and π1(G5) up to isomorphism. Given index n, we calculate the numbers of subgroups and the numbers of conjugacy classes of subgroups for each isomorphism type and provide the Dirichlet generating functions for the above sequences.
AB - There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of n-fold coverings over the orientable Euclidean manifolds G3 and G5, and calculate the numbers of non-equivalent coverings of each type. The manifolds G3 and G5 are uniquely determined among other forms by their homology groups H1(G3)=Z3×Z and H1(G5)=Z. We classify subgroups in the fundamental groups π1(G3) and π1(G5) up to isomorphism. Given index n, we calculate the numbers of subgroups and the numbers of conjugacy classes of subgroups for each isomorphism type and provide the Dirichlet generating functions for the above sequences.
KW - Crystallographic group
KW - Euclidean form
KW - Flat 3-manifold
KW - Non-equivalent coverings
KW - Platycosm
KW - NONEQUIVALENT COVERINGS
KW - REPRESENTATIONS
KW - SUBGROUPS
KW - SURFACES
UR - http://www.scopus.com/inward/record.url?scp=85085338471&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2020.05.010
DO - 10.1016/j.jalgebra.2020.05.010
M3 - Article
AN - SCOPUS:85085338471
VL - 560
SP - 48
EP - 66
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -
ID: 24389559