Related papers: Complexity of virtual 3-manifolds
We compute for all orientable irreducible geometric 3-manifolds certain complexity functions that approximate from above Matveev's natural complexity, known to be equal to the minimal number of tetrahedra in a triangulation. We can show…
For a 3-dimensional manifold $M^3$, its complexity $c(M^3)$, introduced by S.Matveev, is the minimal number of vertices of an almost simple spine of $M^3$; in many cases it is equal to the minimal number of tetrahedra in a singular…
We give a summary of known results on Matveev's complexity of compact 3-manifolds. The only relevant new result is the classification of all closed orientable irreducible 3-manifolds of complexity 10.
The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In…
We extend Matveev's theory of complexity for 3-manifolds, based on simple spines, to (closed, orientable, locally orientable) 3-orbifolds. We prove naturality and finiteness for irreducible 3-orbifolds, and, with certain restrictions and…
By means of a slight modification of the notion of GM-complexity, the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing…
There are found exact values of (Matveev) complexity for the 2-parameter family of hyperbolic 3-manifolds with boundary constructed by Paoluzzi and Zimmermann. Moreover, $\epsilon$-invariants for these manifolds are calculated.
We describe an algorithm which has enabled us to give a complete list, without repetitions, of all closed oriented irreducible 3-manifolds of complexity up to 9. More interestingly, we have actually been able to give a "name" to each such…
We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes…
A special spine of a three-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact three-dimensional manifold M with connected nonempty boundary has a…
We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils…
We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting…
Using the theory of hyperbolic manifolds with totally geodesic boundary, we provide for every integer n greater than 1 a class of such manifolds all having Matveev complexity equal to n and Heegaard genus equal to n+1. All the elements of…
The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev…
We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which…
We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.
We find the exact values of complexity for an infinite series of 3-manifolds. Namely, by calculating hyperbolic volumes, we show that c(N_n)=2n, where $c$ is the complexity of a 3-manifold and N_n is the total space of the punctured torus…
Quantum invariants in low dimensional topology offer a wide variety of valuable invariants of knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is…
We define a relative version of the Turaev-Viro invariants for an ideally triangulated compact 3-manifold with non-empty boundary and a coloring on the edges, generalizing the Turaev-Viro invariants [35] of the manifold. We also propose the…
The triangulation complexity of a closed orientable 3-manifold is the minimal number of tetrahedra in any triangulation of the manifold. The main theorem of the paper gives upper and lower bounds on the triangulation complexity of any…