Minimal triangulations for an infinite family of lens spaces

Abstract

The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein in earlier work, and, unless the lens space is L(3,1), a layered triangulation with the minimal number of tetrahedra was shown to be unique and termed its "minimal layered triangulation." This paper proves that for each integer n>1, the minimal layered triangulation of the lens space L(2n,1) is its unique minimal triangulation. More generally, the minimal triangulations (and hence the complexity) are determined for an infinite family of lens spaces containing the lens spaces L(2n,1).

32 pages, 6 figures

References in corpus (2)

• Layered-triangulations of 3-manifolds
• Two-sided asymptotic bounds for the complexity of some closed hyperbolic three-manifolds

Cited by in corpus (21)

• Coverings and Minimal Triangulations of 3-Manifolds
• The complexity of the normal surface solution space
• A note about complexity of lens spaces
• The simplicial volume of 3-manifolds with boundary
• Systolic geometry and simplicial complexity for groups
• The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces
• Z2-Thurston Norm and Complexity of 3-Manifolds, II
• On minimal ideal triangulations of cusped hyperbolic 3-manifolds
• Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams
• Even triangulations of n-dimensional pseudo-manifolds
• The triangulation complexity of fibred 3-manifolds
• Bounds for the genus of a normal surface
• Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities
• Topological Surgery and its Dynamics
• Generalized Mom-structures and ideal triangulations of 3-manifolds with non-spherical boundary
• Complexity of 3-manifolds obtained by Dehn filling
• Slope norm and an algorithm to compute the crosscap number
• A new family of triangulations of $\mathbb{R}{P}^d$
• Systolic volume and complexity of 3-manifolds
• Geometrically incompressible non-orientable closed surfaces in lens spaces
• Three-dimensional manifolds with poor spines