29 citations · 123 across the 17 of their papers we have counts for
18 papers · 1 filter
Estimating trisection genus via gem theory
Maria Rita Casali, Paola Cristofori
Gems are a particular type of edge-colored graphs, dual to colored triangulations, which represent compact PL-manifolds of arbitrary dimension, both in the closed and boundary case…
Kirby diagrams, trisections and gems of PL 4-manifolds: relationships, results and open problems
Maria Rita Casali, Paola Cristofori
We review the main achievements regarding the interactions between gem theory (which makes use of edge-colored graphs to represent PL-manifolds of arbitrary dimension) and both the…
Trisections of PL 4-manifolds arising from colored triangulations
Maria Rita Casali, Paola Cristofori
The purpose of the present paper is twofold: firstly to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulat…
Kirby diagrams and 5-colored graphs representing compact 4-manifolds
Maria Rita Casali, Paola Cristofori
It is well-known that in dimension 4 any framed link uniquely represents the PL 4-manifold obtained from by adding 2-handles along . Moreove…
Compact 4-manifolds admitting special handle decompositions
Maria Rita Casali, Paola Cristofori
In this paper we study colored triangulations of compact PL 4-manifolds with empty or connected boundary which induce handle decompositions lacking in 1-handles or in 1- and 3-hand…
Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants
Maria Rita Casali, Paola Cristofori, Carlo Gagliardi
The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL -manifolds with empty or connected boundary, called {\it s…
Classifying compact 4-manifolds via generalized regular genus and G-degree
M. R. Casali, P. Cristofori
(d+1)-colored graphs, i.e. edge-colored graphs that are (d+1)-regular, have already been proved to be a useful representation tool for compact PL d-manifolds, thus extending the th…
Gem-induced trisections of compact PL -manifolds
Maria Rita Casali, Paola Cristofori
The idea of studying trisections of closed smooth -manifolds via (singular) triangulations, endowed with a suitable vertex-labelling by three colors, is due to Bell, Hass, Rubin…
Combinatorial properties of the G-degree
Maria Rita Casali, Luigi Grasselli
A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (as a possible approach to the…
G-degree for singular manifolds
Maria Rita Casali, Paola Cristofori, Luigi Grasselli
The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. The present paper studies the properties of the G-degree for the large class o…
Lower bounds for regular genus and gem-complexity of PL 4-manifolds
Biplab Basak, Maria Rita Casali
Within crystallization theory, two interesting PL invariants for -manifolds have been introduced and studied, namely {\it gem-complexity} and {\it regular genus}. In the present…
PL 4-manifolds admitting simple crystallizations: framed links and regular genus
M. R. Casali, P. Cristofori, C. Gagliardi
Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simp…
Cataloguing PL 4-manifolds by gem-complexity
M. R. Casali, P. Cristofori
We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements a…
A note about complexity of lens spaces
Maria Rita Casali, Paola Cristofori
Within crystallization theory, (Matveev's) complexity of a 3-manifold can be estimated by means of the combinatorial notion of GM-complexity. In this paper, we prove that the GM-co…
Computing Matveev's complexity via crystallization theory: the boundary case
Maria Rita Casali, Paola Cristofori
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…
Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams
Maria Rita Casali, Paola Cristofori, Michele Mulazzani
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 crystall…
A catalogue of orientable 3-manifolds triangulated by 30 coloured tetrahedra
M. R. Casali, P. Cristofori
The present paper follows the computational approach to 3-manifold classification via edge-coloured graphs, already performed by several authors with respect to orientable 3-manifo…
Computing Matveev's complexity via crystallization theory: the orientable case
M. R. Casali, P. Cristofori
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 or…