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

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11 papers · 1 filter

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.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.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.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.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.