Expoential bounds on the number of causal triangulations

Abstract

We prove that the number of combinatorially distinct causal 3-dimensional triangulations homeomorphic to the 3-dimensional sphere is bounded by an exponential function of the number of tetrahedra. It is also proven that the number of combinatorially distinct causal 4-dimensional triangulations homeomorphic to the 4-sphere is bounded by an exponential function of the number of 4-simplices provided the number of all combinatorially distinct triangulations of the 3-sphere is bounded by an exponential function of the number of tetrahedra.

30 pages, 9 figures

References in corpus (2)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Nonperturbative Quantum Gravity

Cited by in corpus (6)

• Characteristics of the new phase in CDT
• On the number of coloured triangulations of $d$-manifolds
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Combinatorial Cell Complexes: Duality, reconstruction and causal cobordisms
• Landau Theory of Causal Dynamical Triangulations
• The structure of spatial slices of three-dimensional causal triangulations