Browse Teach Curate

Classification of Non-orientable 3-Manifolds of Surface-Complexity One

Establishes that exactly four closed non-orientable P2-irreducible 3-manifolds have surface-complexity (equivalently cubic-complexity) one, and that all four are flat manifolds. Students learn how a one-cube cubulation is converted into a triangulation through four combinatorial blocks, and how bounding Matveev complexity rules out the remaining candidate, the Sol torus bundle.

Data Text

Non-orientable 3-manifolds of surface-complexity one Gennaro Amendola∗ Abstract We classify all

This paper classifies the closed non-orientable P2-irreducible 3-manifolds that admit a cubulation with a single cube (surface-complexity, equivalently cubic-complexity, equal to one), proving there …