2021/07/07 by Nikolay Abrosimov, Abrosimov, Nikolay, A. G. Kolpakov +3
Computer Science · Mathematics · #11R04 #57K10 #57M50 #Artificial Intelligence in Games #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2107.03275
openalex publication_date 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. This stands in contrast to hyperbolic volumes whose number-theoretic nature is usually quite complicated.