Research output: Contribution to journal › Article › peer-review
Matveev in 2009 introduced the notion of virtual 3-manifold, which generalizes the classical notion of 3-manifold. A virtual 3-manifold is an equivalence class of so-called special polyhedra. Each virtual 3-manifold determines a 3-manifold with nonempty boundary and ℝP2-singularities. Many invariants of manifolds, such as Turaev–Viro invariants, can be extended to virtual 3-manifolds. The complexity of a virtual 3-manifold is k if its equivalence class contains a special polyhedron with k true vertices and contains no special polyhedra with fewer true vertices. In this paper, we give a complete list of virtual 3-manifolds of complexity 1 and present two-sided bounds for the number of virtual 3-manifolds of complexity 2. The question of the complete classification for virtual 3-manifolds of complexity 2 remains open.
Original language | English |
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Pages (from-to) | S154-S160 |
Number of pages | 7 |
Journal | Proceedings of the Steklov Institute of Mathematics |
Volume | 304 |
DOIs | |
State | Published - 1 Apr 2019 |
ID: 49856293