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The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5. / Chelnokov, Grigory; Mednykh, Alexander.

In: Journal of Algebra, Vol. 560, 15.10.2020, p. 48-66.

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

Harvard

Chelnokov, G & Mednykh, A 2020, 'The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5', Journal of Algebra, vol. 560, pp. 48-66. https://doi.org/10.1016/j.jalgebra.2020.05.010

APA

Chelnokov, G., & Mednykh, A. (2020). The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5. Journal of Algebra, 560, 48-66. https://doi.org/10.1016/j.jalgebra.2020.05.010

Vancouver

Chelnokov G, Mednykh A. The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5. Journal of Algebra. 2020 Oct 15;560:48-66. doi: 10.1016/j.jalgebra.2020.05.010

Author

Chelnokov, Grigory ; Mednykh, Alexander. / The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5. In: Journal of Algebra. 2020 ; Vol. 560. pp. 48-66.

BibTeX

@article{5e8b1f9371c54acb8371860b8800ca66,
title = "The enumeration of coverings of closed orientable Euclidean manifolds G3 and G5",
abstract = "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.",
keywords = "Crystallographic group, Euclidean form, Flat 3-manifold, Non-equivalent coverings, Platycosm, NONEQUIVALENT COVERINGS, REPRESENTATIONS, SUBGROUPS, SURFACES",
author = "Grigory Chelnokov and Alexander Mednykh",
year = "2020",
month = oct,
day = "15",
doi = "10.1016/j.jalgebra.2020.05.010",
language = "English",
volume = "560",
pages = "48--66",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

RIS

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