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Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.

Classical and quantum dilogarithmic invariants of flat $P S L (2, ℂ)$ -bundles over 3-manifolds.

Baseilhac, Stéphane, Benedetti, Riccardo (2005)

Geometry & Topology

Coloured knots and permutations representing 3-manifolds.

Grasselli, Luigi (1996)

Mathematica Pannonica

Combinatorial 3-manifolds with 10 vertices.

Lutz, Frank H. (2008)

Beiträge zur Algebra und Geometrie

Compactification via le spectre réel d’espaces des classes de représentation dans SO $(n, 1)$

Taoufik Bouzoubaa (1994)

Annales de l'institut Fourier

Soit $Γ$ un groupe de type fini non élémentaire. On note $D^{n} (Γ)$ l’ensemble des structures hyperboliques de dimension $n$ sur $Γ$ . $D^{n} (Γ)$ peut se réaliser comme fermé dans un espace semi-algébrique qui admet une compactification naturelle par le spectre réel. On note ${\overline{D^{n} (Γ)}}^{sp}$ le compactifié via le $\underline{spectre}$ réel de $D^{n} (Γ)$ . L’objet de cet article est de décrire les points ajoutés dans ${\overline{D^{n} (Γ)}}^{sp}$ . La compactification obtenue de cette manière permet d’interpréter “les points frontières” comme des représentations de $Γ$ dans ${SO}_{F}^{+} (n, 1)$ où $F (\supset ℝ)$ est un corps réel...

Crystallizations of generalized Neuwirth manifolds.

Luigi Grasselli, Salvina Piccarreta (1997)

Forum mathematicum

Cubulations, immersions, mappability and a problem of Habegger

Louis Funar (1999)

Annales scientifiques de l'École Normale Supérieure

Describing toric varieties and their equivariant cohomology

Matthias Franz (2010)

Colloquium Mathematicae

Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even...

Discrete Morse inequalities on infinite graphs.

Ayala, Rafael, Fernández, Luis M., Vilches, José A. (2009)

The Electronic Journal of Combinatorics [electronic only]

Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.

Maria Rita Casali (2004)

Revista Matemática Complutense

The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs.In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing...

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Displaying 1 – 20 of 60

A combinatorial characterization of 4-dimensional handlebodies.

A combinatorial theorem for a symmetric triangulation of the sphere $S^{2}$

A graph-theoretical representation of PL-manifolds - A survey on crystallizations.

A short proof of the uniqueness of Kühnel's 9-vertex complex projective plane.

A simpler construction of volume polynomials for a polyhedron.

A Total Whitehead Torsion Obstruction to Fibering over the Circle.

Absolute subcomplexes

An equivalence criterion for 3-manifolds.