arXiv subjects

Donggyun Seo

Publications and source records attributed to Donggyun Seo.

10 recordsLinked to original sources

arXiv2026

Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group

We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a right-angled Artin group. The proof proceeds by analyzing the geometry of spheres, tori, and simple closed curves in a doubled handlebody. Along the way, we establish the bigon--bihedron criterion and an equivalent condition for commuting Dehn twists. Furthermore, we construct a compact topological space on which multi-twists act parabolically, fixing simplices of weighted multicores, and fully irreducible elements act with north-south dynamics.

math.GR↗

arXiv2026

The topology of Schottky spaces in higher dimensions

The marked Schottky space records, up to conjugacy, all actions of a free group of fixed rank as a Schottky group on hyperbolic space of fixed dimension. In dimension three it is the classical Schottky space covering the moduli space of Riemann surfaces, studied complex-analytically. In higher dimensions each generator gains a rotational parameter, a special orthogonal transformation of the directions normal to its axis, with no classical analogue. Our main theorem treats the borderline dimension, twice the rank: there a dense open part of the space has fundamental group a product of cyclic groups of order two, one per generator, yet the whole space is simply connected, since each such loop contracts through the most degenerate configurations. As a consequence, any two Schottky groups of the same rank in this borderline dimension are quasiconformally isotopic, partially answering a question of Kapovich. We also show that a rotationally symmetric core is a strong deformation retract in every dimension, that this dense open part is homotopy equivalent to a product of special orthogonal groups, and that the analogous locus one dimension below has two connected components.

math.GT↗

arXiv2026

A note on the Burnside problem for homeomorphism groups of manifolds

This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely when the surface is not the sphere, torus, projective plane, or Klein bottle. An extension argument based on the Tits alternative for mapping class groups then implies that every finitely generated periodic subgroup of the full homeomorphism group is finite for all surfaces outside this exceptional list, recovering and extending a theorem of Guelman and Liousse to non-orientable surfaces. For the circle, we prove that every finitely generated periodic subgroup of its homeomorphism group is finite and cyclic. We close with remarks on manifolds with boundary and open questions on the Burnside problem for hyperbolic three-manifolds and doubled handlebodies.

math.GT↗

arXiv2026

The Pants Graph of a Free Group

We introduce the concept of a pants decomposition for a finitely generated free group and construct the corresponding pants graph. A pants decomposition of a free group leads to the formation of a simplicial graph, referred to as the pants graph of a free group, consisting of all possible pants decompositions. The natural isometric action of the outer automorphism group of the free group on the pants graph induces a coarsely surjective orbit map. Additionally, we construct a coarsely Lipschitz map from the pants graph to the free splitting complex. These results imply that the pants graph of a free group is both connected and unbounded.

math.GR↗

arXiv2026

A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation

Severe accident analysis using system-level codes such as MELCOR is indispensable for nuclear safety assessment, yet the computational cost of repeated simulations poses a significant bottleneck for parametric studies and uncertainty quantification. Existing surrogate models accelerate these analyses but depend on large volumes of simulation data, while physics-informed neural networks (PINNs) enable data-free training but must be retrained for every change in problem parameters. This study addresses both limitations by developing the Parameterized PINNs coupled with FDM (P2F) method, a node-assigned hybrid framework for MELCOR's Control Volume Hydrodynamics/Flow Path (CVH/FP) module. In the P2F method, a parameterized Node-Assigned PINN (NA-PINN) accepts the water-level difference, initial velocity, and time as inputs, learning a solution manifold so that a single trained network serves as a data-free surrogate for the momentum conservation equation across all flow paths without retraining. This PINN is coupled with a finite difference method (FDM) solver that advances the mass conservation equation at each time step, ensuring exact discrete mass conservation while replacing the iterative nonlinear momentum solve with a single forward pass. Verification on a six-tank gravity-driven draining scenario yields a water level mean absolute error of $7.85 \times 10^{-5}$ m and a velocity mean absolute error of $3.21 \times 10^{-3}$ m/s under the nominal condition with $Δt = 1.0$ s. The framework maintains consistent accuracy across time steps ranging from 0.2 to 1.0 s and generalizes to five distinct initial conditions, all without retraining or simulation data. This work introduces a numerical coupling methodology for integrating parameterized PINNs with FDM within a nuclear thermal-hydraulic system code framework.

cs.LG↗

arXiv2025

Percolation in acylindrically hyperbolic groups

Let $G$ be an acylindrically hyperbolic group. We prove that Bernoulli bond percolation on every Cayley graph of $G$ has a nonuniqueness phase, in which there are infinitely many infinite clusters. This generalizes Hutchcroft's result for Gromov hyperbolic graphs to relatively hyperbolic groups, mapping class groups and rank-1 CAT(0) groups for example.

math.GR↗

arXiv2023

Liftable automorphisms of right-angled Artin groups

Given a regular covering map $φ:Λ\to Γ$ of graphs, we investigate the subgroup $\operatorname{LAut}(φ)$ of the automorphism group $\operatorname{Aut}(A_Γ)$ of the right-angled Artin group $A_Γ$. This subgroup comprises all automorphisms that can be lifted to automorphisms of $A_Λ$. We first show that $\operatorname{LAut}(φ)$ is generated by a finite subset of Laurence's elementary automorphisms. For the subgroup $\operatorname{FAut}(φ)$ of $\operatorname{Aut}(A_Λ)$, which consists of lifts of automorphisms in $\operatorname{LAut}(φ)$, there exists a natural homomorphism $\operatorname{FAut}(φ)\to\operatorname{LAut}(φ)$ induced by $φ$. We then show that the kernel of this homomorphism is virtually a subgroup of the Torelli subgroup $\operatorname{IA}(A_Λ)$ and deduce a short exact sequence reminiscent of results from the Birman--Hilden theory for surfaces.

math.GR↗

arXiv2023

Uniform difference between the length spectra of Out(F2) and the genus two handlebody group

In this paper, we analyze the natural homomorphism from the genus g handlebody group to the outer automorphism group of the free group with rank g, in terms of length spectra. In general, the preimage of each fully irreducible outer automorphism contains a potentially infinite number of pseudo-Anosov mapping classes. Our study reveals a crucial relationship: for any pseudo-Anosov map in this preimage, its stretch factor must equal or exceed that of the corresponding fully irreducible outer automorphism. Notably, in the case of genus two, we establish that the minimum stretch factor among these pseudo-Anosov maps is less than ten times the stretch factor of the fully irreducible outer automorphism. These results partially address a question by Hensel and have practical implications, including a lower bound for the geodesic counting problem in the genus two handlebody group.

math.GT↗

arXiv2022

On the finiteness property of hyperbolic simplicial actions: the right-angled Artin groups and their extension graphs

We study the right-angled Artin group action on the extension graph. We show that this action satisfies a certain finiteness property, which is a variation of a condition introduced by Delzant and Bowditch. As an application we show that the asymptotic translation lengths of elements of a given right-angled Artin group are always rational and once the defining graph has girth at least 6, they have a common denominator. We construct explicit examples which show the denominator of the asymptotic translation length of such an action can be arbitrary. We also observe that if either an element has a small syllable length or the defining graph for the right-angled Artin group is a tree then the asymptotic translation lengths are integers.

math.GR↗

arXiv2019

Powers of Dehn twists generating right-angled Artin groups

We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if $\mathcal{F}$ is a finite collection of pairwise distinct simple closed curves on a finite type surface and if $N$ denotes the maximum of the intersection numbers of all pairs of curves in $\mathcal{F}$, then we prove that $\{T_γ^n \,\vert\, γ\in \mathcal{F} \}$ generates a right-angled Artin group for all $n \geq N^2 + N + 3$. This extends a previous result of Koberda, who proved the existence of a bound possibly depending on the underlying hyperbolic structure of the surface. In the course of the proof, we obtain a universal bound depending only on the topological type of the surface in certain cases, which partially answers a question due to Koberda.

math.GR↗