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.
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