ON THE COVERINGS OF HANTZSCHE-WENDT MANIFOLD Full article
| Journal |
Tohoku Mathematical Journal
ISSN: 0040-8735 |
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| Output data | Year: 2022, Volume: 74, Number: 2, Pages: 313-327 Pages count : 15 DOI: 10.2748/tmj.20210308 | ||||||
| Tags | crystallographic; Euclidean form; flat 3-manifold; non-equivalent coverings; platycosm | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0007 |
Abstract:
There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable G1, . . . , G6 and four are non-orientable B1, . . . , B4. In the present paper we investigate the manifold G6, also known as Hantzsche-Wendt manifold; this is the unique Euclidean 3-form with finite first homology group H1(G6) = Z24 . The aim of this paper is to describe all types of n-fold coverings over G6 and calculate the numbers of non-equivalent coverings of each type. We classify subgroups in the fundamental group π1(G6) 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 series for the above sequences.
Cite:
Chelnokov G.
, Mednykh A.
ON THE COVERINGS OF HANTZSCHE-WENDT MANIFOLD
Tohoku Mathematical Journal. 2022. V.74. N2. P.313-327. DOI: 10.2748/tmj.20210308 WOS Scopus РИНЦ OpenAlex
ON THE COVERINGS OF HANTZSCHE-WENDT MANIFOLD
Tohoku Mathematical Journal. 2022. V.74. N2. P.313-327. DOI: 10.2748/tmj.20210308 WOS Scopus РИНЦ OpenAlex
Dates:
| Published online: | Jun 6, 2022 |
Identifiers:
| Web of science: | WOS:000828223600009 |
| Scopus: | 2-s2.0-85135184687 |
| Elibrary: | 55778579 |
| OpenAlex: | W3086594237 |