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On the coverings of closed orientable Euclidean manifolds G(2) and G(4). / Chelnokov, Grigory; Mednykh, Alexander.

In: Communications in Algebra, Vol. 48, No. 7, 02.07.2020, p. 2725-2739.

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

Harvard

Chelnokov, G & Mednykh, A 2020, 'On the coverings of closed orientable Euclidean manifolds G(2) and G(4)', Communications in Algebra, vol. 48, no. 7, pp. 2725-2739. https://doi.org/10.1080/00927872.2019.1705468

APA

Chelnokov, G., & Mednykh, A. (2020). On the coverings of closed orientable Euclidean manifolds G(2) and G(4). Communications in Algebra, 48(7), 2725-2739. https://doi.org/10.1080/00927872.2019.1705468

Vancouver

Chelnokov G, Mednykh A. On the coverings of closed orientable Euclidean manifolds G(2) and G(4). Communications in Algebra. 2020 Jul 2;48(7):2725-2739. doi: 10.1080/00927872.2019.1705468

Author

Chelnokov, Grigory ; Mednykh, Alexander. / On the coverings of closed orientable Euclidean manifolds G(2) and G(4). In: Communications in Algebra. 2020 ; Vol. 48, No. 7. pp. 2725-2739.

BibTeX

@article{fa3132a499aa47859ef81b63ba4685cc,
title = "On the coverings of closed orientable Euclidean manifolds G(2) and G(4)",
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 orientable Euclidean manifolds G(2) and G(4) and calculate the numbers of nonequivalent coverings of each type. We classify subgroups in the fundamental groups pi(1)(G(2)) and pi(1)(G(4)) up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index n. The manifolds and are uniquely determined among the others orientable forms by their homology groups H-1(G(2)) = Z(2) x Z(2) x Z and H-1(G4) = Z(2) x Z.",
keywords = "Crystallographic group, Euclidean form, flat 3-manifold, nonequivalent coverings, platycosm, SUBGROUPS, ENUMERATING REPRESENTATIONS",
author = "Grigory Chelnokov and Alexander Mednykh",
note = "Publisher Copyright: {\textcopyright} 2020, {\textcopyright} 2020 Taylor & Francis Group, LLC. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = jul,
day = "2",
doi = "10.1080/00927872.2019.1705468",
language = "English",
volume = "48",
pages = "2725--2739",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "7",

}

RIS

TY - JOUR

T1 - On the coverings of closed orientable Euclidean manifolds G(2) and G(4)

AU - Chelnokov, Grigory

AU - Mednykh, Alexander

N1 - Publisher Copyright: © 2020, © 2020 Taylor & Francis Group, LLC. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/7/2

Y1 - 2020/7/2

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 orientable Euclidean manifolds G(2) and G(4) and calculate the numbers of nonequivalent coverings of each type. We classify subgroups in the fundamental groups pi(1)(G(2)) and pi(1)(G(4)) up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index n. The manifolds and are uniquely determined among the others orientable forms by their homology groups H-1(G(2)) = Z(2) x Z(2) x Z and H-1(G4) = Z(2) x Z.

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 orientable Euclidean manifolds G(2) and G(4) and calculate the numbers of nonequivalent coverings of each type. We classify subgroups in the fundamental groups pi(1)(G(2)) and pi(1)(G(4)) up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index n. The manifolds and are uniquely determined among the others orientable forms by their homology groups H-1(G(2)) = Z(2) x Z(2) x Z and H-1(G4) = Z(2) x Z.

KW - Crystallographic group

KW - Euclidean form

KW - flat 3-manifold

KW - nonequivalent coverings

KW - platycosm

KW - SUBGROUPS

KW - ENUMERATING REPRESENTATIONS

UR - http://www.scopus.com/inward/record.url?scp=85083656824&partnerID=8YFLogxK

U2 - 10.1080/00927872.2019.1705468

DO - 10.1080/00927872.2019.1705468

M3 - Article

AN - SCOPUS:85083656824

VL - 48

SP - 2725

EP - 2739

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 7

ER -

ID: 24076616