2025/03/23 by Repovš, Dušan D., Vesnin, Andrei Yu.
#52B10 #57K10 #57K32 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2503.17974
An n-component link L is said to be Brunnian if it is non-trivial but every proper sublink of L is trivial. The simplest and best known example of a hyperbolic Brunnian link is the 3-component link known as "Borromean rings". For n≥ 2, we introduce an infinite family of n-component Brunnian links with positive integer parameters Br(k1, …, kn) that generalize examples constructed by Debrunner in 1964. We are interested in hyperbolic invariants of 3-manifolds S3 ∖ Br(k1, …, kn) and we obtain upper bounds for their volumes. Our approach is based on Dehn fillings on cusped manifolds with volumes related to volumes of ideal right-angled hyperbolic antiprisms.