Philippe Tranchida

activity

20192026

most citedTopological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori

1 citations · 2 across the 12 of their papers we have counts for

collaborators

16 papers

math.GR2026

Hypertopes with prescribed diagram symmetries

Dimitri Leemans, Pablo Spiga, Philippe Tranchida

Let $G$ be a finite connected simple graph with at least two vertices. We construct a finite regular hypertope $Γ$ whose diagram is the graph $G$ with every edg…

math.CO2026

Coset geometries acting on their elements: The $j$ -diagonals twisting

Claudio Alexandre Piedade, Philippe Tranchida

Let $β$ be a coset incidence system and fix a type $j$ . We use the orbits of the group of $β$ on pairs of distinct $j$ -elements to define a Coxeter graph. The action on the $j$ -ele…

math.GR2026

The geometry of wreath and semi-direct products

Claudio Alexandre Piedade, Philippe Tranchida

Coset geometries are incidence geometries constructed from a group $G$ and a system of subgroups $(G_{i})_{i \in I}$ of subgroups of $G$ . For any algebraic group operation, it is the…

math.GR2025

Groups represented by incidence geometries

Dimitri Leemans, Klara Stokes, Philippe Tranchida

The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. Mo…

math.GR2025

From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries

Claudio Alexandre Piedade, Philippe Tranchida

Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry. In this article, we build upon t…

math.CO2025

Geometries with trialities arising from linear spaces

Rémi Delaby, Dimitri Leemans, Philippe Tranchida

A triality is a sort of super-symmetry that exchanges the types of the elements of an incidence geometry in cycles of length three. Although geometries with trialities exhibit fasc…

math.GR2024

Triples of involutions in PGL(2,q) and their incidence geometries

Philippe Tranchida

For $q = p^{n}$ with $p$ an odd prime, the projective linear group $P G L (2, q)$ can be seen as the stabilizer of a conic $O$ in a projective plane $π = P G (2, q)$ . In that setting, involu…

math.CO2024

Constructing new geometries: a generalized approach to halving for hypertopes

Claudio Alexandre Piedade, Philippe Tranchida

Given a residually connected incidence geometry $Γ$ that satisfies two conditions, denoted $(B_{1})$ and $(B_{2})$ , we construct a new geometry $H (Γ)$ with properties similar to those…

math.GR2023

Flag transitive geometries with trialities and no dualities coming from Suzuki groups

Dimitri Leemans, Klara Stokes, Philippe Tranchida

Recently, Leemans and Stokes constructed an infinite family of incidence geometries admitting trialities but no dualities from the groups PSL(2,q) (where $q = p^{3 n}$ with $p$ a prim…

math.GR2023

On trialities and their absolute geometries

Dimitri Leemans, Klara Stokes, Philippe Tranchida

We introduce the notion of moving absolute geometry of a geometry with triality and show that, in the classical case where the triality is of type $(I_{σ})$ and the absolute geometry…

math.GT2023

Thurston unit ball of a family of $n$ -chained links and their fibered face

Juhun Baik, Philippe Tranchida

We determine the Thurston unit ball of a family of $n$ -chained link, denoted by $C (n, p)$ , where $n$ is the number of link components and $p$ is the number of twists. When $p$ is st…

math.GT2022★ 1 cited

Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori

Hyungryul Baik, Juhun Baik, Changsub Kim +1

We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surfac…

math.GR2022

Liftable automorphisms of right-angled Artin groups

Sangrok Oh, Donggyun Seo, Philippe Tranchida

Given a regular covering map $φ : Λ \to Γ$ of graphs, we investigate the subgroup $LAut (φ)$ of the automorphism group $Aut (A_{Γ})$ of the right-angled Arti…

math.GR2021★ 1 cited

Automorphism and outer automorphism groups of Right-angled Artin groups are not relatively hyperbolic

Junseok Kim, Sangrok Oh, Philippe Tranchida

We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least 3 vertices are not relatively hyperbolic. We then show that the outer automorp…

math.GR2019

A new algorithm to classify chiral polytopes with a given automorphism group

Francis Buekenhout, Dimitri Leemans, Philippe Tranchida

We present a new algorithm to compute all the chiral polytopes that have a given group $G$ as full automorphism group. This algorithm uses a new set of generators that characterize…

math.GR2019

On residual connectedness in chiral geometries

Dimitri Leemans, Philippe Tranchida

We show that a chiral coset geometry constructed from a $C^{+}$ -group necessarily satisfies residual connectedness and is therefore a hypertope.

Hypertopes with prescribed diagram symmetries

Coset geometries acting on their elements: The j-diagonals twisting

The geometry of wreath and semi-direct products

Groups represented by incidence geometries

From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries

Geometries with trialities arising from linear spaces

Triples of involutions in PGL(2,q) and their incidence geometries

Constructing new geometries: a generalized approach to halving for hypertopes

Flag transitive geometries with trialities and no dualities coming from Suzuki groups

On trialities and their absolute geometries

Thurston unit ball of a family of n-chained links and their fibered face

Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori

Liftable automorphisms of right-angled Artin groups

Automorphism and outer automorphism groups of Right-angled Artin groups are not relatively hyperbolic

A new algorithm to classify chiral polytopes with a given automorphism group

On residual connectedness in chiral geometries

Coset geometries acting on their elements: The $j$ -diagonals twisting

Thurston unit ball of a family of $n$ -chained links and their fibered face