11 citations · 15 across the 7 of their papers we have counts for
6 papers · 1 filter
Infinitely many arithmetic hyperbolic rational homology 3-spheres that bound geometrically
Leonardo Ferrari, Alexander Kolpakov, Alan W. Reid
In this paper we provide the first examples of arithmetic hyperbolic 3-manifolds that are rational homology spheres and bound geometrically either compact or cusped hyperbolic 4-ma…
Euclidean volumes of hyperbolic knots
Nikolay Abrosimov, Alexander Kolpakov, Alexander Mednykh
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 th…
On faces of quasi-arithmetic Coxeter polytopes
Nikolay Bogachev, Alexander Kolpakov
We prove that each lower-dimensional face of a quasi-arithmetic Coxeter polytope, which happens to be itself a Coxeter polytope, is also quasi-arithmetic. We also provide a suffici…
A hyperbolic counterpart to Rokhlin's cobordism theorem
Michelle Chu, Alexander Kolpakov
The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic -manifolds that are geometric boundaries of compact o…
Many cusped hyperbolic 3-manifolds do not bound geometrically
Alexander Kolpakov, Alan W. Reid, Stefano Riolo
In this note, we show that there exist cusped hyperbolic -manifolds that embed geodesically, but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial pr…
Combinatorial decompositions, Kirillov-Reshetikhin invariants and the Volume Conjecture for hyperbolic polyhedra
Alexander Kolpakov, Jun Murakami
We suggest a method of computing volume for a simple polytope in three-dimensional hyperbolic space . This method combines the combinatorial reduction of as a…