A new combinatorial class of 3-manifold triangulations

2013/12/18 by Feng Luo, Stephan Tillmann, Luo, Feng +1
Mathematics · #57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57N10

paper · pdf · doi:10.48550/arxiv.1312.5087

28 pages, 23 figures; colour printing recommended; to appear in AJM

arxiv created 2015/12/22 · arxiv updated 2015/12/23

Abstract

We define a new combinatorial class of triangulations of closed 3-manifolds, satisfying a weak version of 0-efficiency combined with a weak version of minimality, and study them using twisted squares. As an application, we obtain strong restrictions on the topology of a 3-manifold from the existence of non-smooth maxima of the volume function on the space of circle-valued angle structures.

Related

• 0-efficient triangulations of 3-manifolds
• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
• Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds
• Poor ideal three-edge triangulations are minimal
• Minimal Triangulations of Manifolds