On hyperelliptic Euclidean 3-manifolds

On hyperelliptic Euclidean 3-manifolds Full article

Journal

Journal of Knot Theory and its Ramifications
ISSN: 0218-2165

Output data

Year: 2021, Volume: 30, Number: 10, Article number : 21400015, Pages count : DOI: 10.1142/S0218216521400010

Tags

branched covering; Euclidean form; fundamental group; homology group; hyperelliptic manifold; π -orbifold

Authors

Mednykh A.D. ^1,2,3 , Vuong B. ^1,3

Affiliations

1	Tomsk State University, Tomsk, 634050, Russian Federation
2	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State University, Novosibirsk, 630090, Russian Federation

In this paper, we study closed orientable Euclidean manifolds which are also known as flat three-dimensional manifolds or just Euclidean 3-forms. Up to homeomorphism, there are six of them. The first one is the three-dimensional torus. In 1972, Fox showed that the 3-torus is not a double branched covering of the 3-sphere. So, it is not a hyperelliptic manifold. In this paper, we show that all the remaining Euclidean 3-forms are hyperelliptic manifolds. © 2021 World Scientific Publishing Company.

Mednykh A.D. , Vuong B.
On hyperelliptic Euclidean 3-manifolds
Journal of Knot Theory and its Ramifications. 2021. V.30. N10. 21400015 . DOI: 10.1142/S0218216521400010 WOS Scopus OpenAlex

Web of science:	WOS:000743509300004
Scopus:	2-s2.0-85121243393
OpenAlex:	W4200038350

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