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On hyperelliptic Euclidean 3-manifolds

A. D. Mednykh

Tomsk State University, Tomsk 634050, Russia

Sobolev Institute of Mathematics, Novosibirsk 630090, Russia

Novosibirsk State University, Novosibirsk 630090, Russia

E-mail Address: smedn@mail.ru

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and

B. Vuong

Tomsk State University, Tomsk 634050, Russia

Novosibirsk State University, Novosibirsk 630090, Russia

E-mail Address: vuonghuubao@live.com

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https://doi.org/10.1142/S0218216521400010Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue: Proceedings of 6th Russian — Chinese Conference on Knot Theory and Related Topics (2nd Part)
Guest Editors: L. Kauffman, A. Vesnin, Z. Yang, Z. Cheng and N. Abrosimov

Abstract

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.

Keywords:

AMSC: 57M50, 57M12, 57M25

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