A Census of Tetrahedral Hyperbolic Manifolds. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Fominykh, Evgeny; Garoufalidis, Stavros; Goerner, Matthias; Tarkaev, Vladimir; Vesnin, Andrei
• Is Part Of: Experimental mathematics. Volume 25:Issue 4(2016)
• Page Start: 466
• Page End: 481
• Publication Date: 2016-10-01
• Subjects: hyperbolic 3-manifolds -- regular ideal tetrahedron -- census -- tetrahedral manifolds -- Bianchi orbifolds; Primary 57N10 -- Secondary 57M25; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: Http://www.tandfonline.com/doi/10.1080/10586458.2015.1114436
• Languages: English
• ISSNs: 1058-6458

Abstract

ABSTRACT: We call a cusped hyperbolic 3-manifold tetrahedral if it can be decomposed into regular ideal tetrahedra. Following an earlier publication by three of the authors, we give a census of all tetrahedral manifolds and all of their combinatorial tetrahedral tessellations with at most 25 (orientable case) and 21 (non-orientable case) tetrahedra. Our isometry classification uses certified canonical cell decompositions (based on work by Dunfield, Hoffman, and Licata) and isomorphism signatures (an improvement of dehydration sequences by Burton). The tetrahedral census comes inRegina as well asSnapPy format, and we illustrate its features.