36 citations · 170 across the 43 of their papers we have counts for
8 papers · 1 filter
Space vectors forming rational angles
Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen +1
We classify all sets of nonzero vectors in such that the angle formed by each pair is a rational multiple of . The special case of four-element subsets lets us cl…
Packable hyperbolic surfaces with symmetries
Maria Dostert, Alexander Kolpakov
We discuss several ways of packing a hyperbolic surface with circles (of either varying radii or all being congruent) or horocycles, and note down some observations related to thei…
Cusps of hyperbolic 4-manifolds and rational homology spheres
Leonardo Ferrari, Alexander Kolpakov, Leone Slavich
In the present paper, we construct a cusped hyperbolic -manifold with all cusp sections homeomorphic to the Hantzsche-Wendt manifold, which is a rational homology sphere. By a r…
The signature of cusped hyperbolic 4-manifolds
Alexander Kolpakov, Stefano Riolo, Steven T. Tschantz
In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic 4-manifold of finite volume, and give some partial results on the geography of such…
Semidefinite programming bounds for the average kissing number
Maria Dostert, Alexander Kolpakov, Fernando Mário de Oliveira Filho
The average kissing number of is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in . We provid…
Kissing number in non-Euclidean spaces of constant sectional curvature
Maria Dostert, Alexander Kolpakov
This paper provides upper and lower bounds on the kissing number of congruent radius spheres in hyperbolic and spherical spaces, for …