Research output: Contribution to journal › Article › peer-review
Euclidean volumes of hyperbolic knots. / Abrosimov, Nikolay; Kolpakov, Alexander; Mednykh, Alexander.
In: Proceedings of the American Mathematical Society, Vol. 152, No. 2, 01.02.2024, p. 869-881.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Euclidean volumes of hyperbolic knots
AU - Abrosimov, Nikolay
AU - Kolpakov, Alexander
AU - Mednykh, Alexander
N1 - Received by the editors September 4, 2021, and, in revised form, August 22, 2022, and November 18, 2022. 2020 Mathematics Subject Classification. Primary 57K10, 57M50, 11R04. The first and third authors were supported by the state contract of Sobolev Institute of Mathematics (project no. FWNF-2022-0005). The second author was supported by the Swiss National Science Foundation (projects PP00P2–170560 and PP00P2–202667).
PY - 2024/2/1
Y1 - 2024/2/1
N2 - The hyperbolic structure on a 3 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.
AB - The hyperbolic structure on a 3 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.
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85181951358&origin=inward&txGid=ba4c84da532144f011d6120be3c1e9df
UR - https://www.mendeley.com/catalogue/cd58b304-cdef-3f40-81f9-8bc36a1f4d27/
U2 - 10.1090/proc/16353
DO - 10.1090/proc/16353
M3 - Article
VL - 152
SP - 869
EP - 881
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 2
ER -
ID: 61294251