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Virtual 3-Manifolds of Complexity 1 and 2.
- Source :
- Proceedings of the Steklov Institute of Mathematics; Apr2019 Supplement 1, Vol. 304 Issue 1, pS154-S160, 7p
- Publication Year :
- 2019
-
Abstract
- 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 ℝP<superscript>2</superscript>-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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00815438
- Volume :
- 304
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the Steklov Institute of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 136861480
- Full Text :
- https://doi.org/10.1134/S0081543819020172