Hyperbolic 4‐manifolds, colourings and mutations. Issue 2 (22nd June 2016) - Kolpakov, Alexander; Slavich, Leone
Abstract : We develop a way of seeing a complete orientable hyperbolic 4‐manifold M as an orbifold cover of a Coxeter polytope P ⊂ H 4 that has a facet colouring. We also develop a way of finding a totally geodesic sub‐manifold N in M, and describing the result of mutations along N . As an application of our method, we construct an example of a complete orientable hyperbolic 4‐manifold X with a single non‐toric cusp and a complete orientable hyperbolic 4‐manifold Y with a single toric cusp. Both X and Y have twice the minimal volume among all complete orientable hyperbolic 4‐manifolds.