Dr. Alexander Kolpakov

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Academic Career Length

18Years (2009-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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3 August 2013 in Geometric and Functional Analysis

Journal Article

Hyperbolic four-manifolds with one cusp

Alexander Kolpakov

Bruno Martelli

6 April 2015 in Proceedings of the American Mathematical Society

Journal Article

Some hyperbolic three-manifolds that bound geometrically

Alexander Kolpakov

Bruno Martelli

Steven Tschantz

A closed connected hyperbolic

n

-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic

(n+1)

-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many manifolds that bound geometrically in every dimension. We construct here infinitely many explicit examples in dimension

n=3

using right-angled dodecahedra and 120-cells and a simple colouring technique introduced by M. Davis and T. Januszkiewicz. Namely, for every

k\geqslant 1

, we build an orientable compact closed 3-manifold tessellated by

16k

right-angled dodecahedra that bounds a 4-manifold tessellated by

32k

right-angled 120-cells. A notable feature of this family is that the ratio between the volumes of the 4-manifolds and their boundary components is constant and, in particular, bounded.