Euclidean volumes of hyperbolic knots

Euclidean volumes of hyperbolic knots Full article

Journal

Proceedings of the American Mathematical Society
ISSN: 0002-9939 , E-ISSN: 1088-6826

Output data

Year: 2024, Volume: 152, Pages: 869-881 Pages count : 13 DOI: 10.1090/proc/16353

Authors

Abrosimov N. ^1,2 , Kolpakov A. ³ , Mednykh A. ^1,2

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University
3	Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000 Neuchâtel, Suisse / Switzerland

Funding (2)

1	Sobolev Institute of Mathematics	FWNF-2022-0005
2	Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok	075-15-2019-1613, 075-15-2022-281

The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an algebraic number, which is reminiscent of Sabitov's theorem (the Bellows Conjecture). This fact also stands in contrast to hyperbolic volumes whose number-theoretic nature is usually quite complicated.

Abrosimov N. , Kolpakov A. , Mednykh A.
Euclidean volumes of hyperbolic knots
Proceedings of the American Mathematical Society. 2024. V.152. P.869-881. DOI: 10.1090/proc/16353 WOS Scopus РИНЦ OpenAlex

Submitted:	Sep 4, 2021
Accepted:	Nov 18, 2022
Published online:	Dec 7, 2023
Published print:	Mar 6, 2024

Web of science:	WOS:001120917300001
Scopus:	2-s2.0-85181951358
Elibrary:	60266777
OpenAlex:	W3182077570

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