Related papers: On Entropy of 3-Dimensional Simplicial Complexes
We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed…
It is proven that the partition function of 3-dimensional simplicial gravity has an exponential upper bound with the following assumption: any three dimensional sphere $S^3$ is constructed by repeated identification of neighboring links and…
We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity.Both the critical coupling and various other quantities show a slow power law approach…
We deduce the appearance of a polymeric phase in 4-dimensional simplicial quantum gravity by varying the values of the coupling constants and discuss the geometric structure of the phase in terms of ergodic moves. A similar result is true…
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…
We extend simulations of simplicial gravity in four dimensions to include {\it degenerate} triangulations and demonstrate that using this ensemble the geometric finite-size effects are much reduced. We provide strong numerical evidence for…
We give a simple combinatoric proof of an exponential upper bound on the number of distinct 3-manifolds that can be constructed by successively identifying nearest neighbour pairs of triangles in the boundary of a simplicial 3-ball and show…
We simulate 4d simplicial gravity for three topologis S4, S3xS1, (S1)^4 and show that the free energy for these three fixed topology ensembles is the same in the thermodynamic limit. We show, that the next-to-leading order corrections, at…
We show that the simplicial volume of a contractible 3-manifold not homeomorphic to $\mathbb{R}^3$ is infinite. As a consequence, the Euclidean space may be characterized as the unique contractible $3$-manifold with vanishing minimal…
We show that non-elliptic prime 3-manifolds satisfy integral approximation for the simplicial volume, i.e., that their simplicial volume equals the stable integral simplicial volume. The proof makes use of integral foliated simplicial…
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present…
We provide a simple characterization of simplicial complexes on few vertices that embed into the $d$-sphere. Namely, a simplicial complex on $d+3$ vertices embeds into the $d$-sphere if and only if its non-faces do not form an intersecting…
I review recent progress in simplicial quantum gravity in three and four dimensions, in particular new results on the phase structure of modified models of dynamical triangulations, the application of a strong-coupling expansion, and the…
We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
The number of configurations of the dynamical triangulation model of 4D euclidean quantum gravity appears to grow faster than exponentially with the volume, with the implication that the system would end up in the crumpled phase for any…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
We study the canonical structure of three-dimensional topologically massive gravity with a cosmological constant, using the full power of Dirac's method for constrained Hamiltonian systems. It is found that the dimension of the physical…
Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M…
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…