Hyperbolic 4‐manifolds, colourings and mutations. Issue 2 (22nd June 2016)

• Record Type: Journal Article
• Authors: Kolpakov, Alexander; Slavich, Leone
• Is Part Of: Proceedings of the London Mathematical Society. Volume 113:Issue 2(2016:Aug.)
• Page Start: 163
• Page End: 184
• Publication Date: 2016-06-22
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdw025
• Languages: English
• ISSNs: 0024-6115

Abstract

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.