The average edge order of triangulations of 3-manifolds with boundary

Tamura, Makoto

doi:10.1090/s0002-9947-98-02014-5

Cited by 2 publications

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar results for 3-manifolds with non-empty boundary were established by Tamura [17,18]. For a related study see also the paper of Walkup [22].…”

Section: Average Ordersupporting

confidence: 77%

On Graph-Theoretical Invariants of Combinatorial Manifolds

Cavicchioli

Spaggiari²

2019

Electron. J. Combin.

View full text Add to dashboard Cite

The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed manifolds up to piecewise-linear (PL) homeomorphism. For this, we use the combinatorial approach to the topology of PL manifolds by means of a special kind of edge-colored graphs, called crystallizations. Within this representation theory, Bracho and Montejano introduced in 1987 a nonnegative numerical invariant, called the reduced complexity, for any closed $n$-dimensional PL manifold. Here we consider this invariant, and extend in this context the concept of average order first introduced by Luo and Stong in 1993, and successively investigated by Tamura in 1996 and 1998. Then we obtain some classification results for closed connected smooth low-dimensional manifolds according to reduced complexity and average order. Finally, we answer to a question posed by Trout in 2013.

show abstract

“…Similar results for 3-manifolds with non-empty boundary were established by Tamura [17,18]. For a related study see also the paper of Walkup [22].…”

Section: Average Ordersupporting

confidence: 77%

On Graph-Theoretical Invariants of Combinatorial Manifolds

Cavicchioli

Spaggiari²

2019

Electron. J. Combin.

View full text Add to dashboard Cite

show abstract

“…What can we say about the possible values of A CR (T )? Thanks to the work of Luo and Stong [20] and Tamura [25], for n = 3 we can say quite a lot. First, some terminology and preliminary results.…”

Section: Global Extrema Of a Cr For N =mentioning

confidence: 99%

Combinatorial Dark Energy

Trout¹

2012

Preprint

View full text Add to dashboard Cite

In this paper, we give a conceptual explanation of dark energy as a small negative residual scalar curvature present even in empty spacetime. This curvature ultimately results from postulating a discrete spacetime geometry, very closely related to that used in the dynamical triangulations approach to quantum gravity. In this model, there are no states which have total scalar curvature exactly zero. Moreover, numerical evidence in dimension three suggests that, at a fixed volume, the number of discrete-spacetime microstates strongly increases with decreasing curvature. Because of the resulting entropic force, any dynamics which push empty spacetime strongly toward zero scalar curvature would instead produce typically observed states with a small negative curvature. This provides a natural explanation for the empirically observed small positive value for the cosmological constant (Λ ≈ 10 −121 in Planck units.) In fact, we derive the very rough estimate Λ ≈ 10 −187 from a simple model containing only the two (highlydegenerate) quantum states with total scalar-curvature closest to zero.

show abstract

The average edge order of triangulations of 3-manifolds with boundary

Cited by 2 publications

References 4 publications

On Graph-Theoretical Invariants of Combinatorial Manifolds

On Graph-Theoretical Invariants of Combinatorial Manifolds

Combinatorial Dark Energy

Contact Info

Product

Resources

About