arXiv research

Embeddings of mapping tori for end-periodic graph maps are proven.

The paper defines and proves the existence of train track maps on graphs of groups.

The paper explores non-amenability in infinite-type surfaces and graphs.

The paper defines when surfaces are homotopy equivalent to graphs and explores their mapping class groups.

Shifts are not type-preserving on surface graphs.

The curve graph and related graphs are hyperbolic and have quasi-tree fibers.

Study of mapping class groups on infinite graphs, focusing on their large-scale geometry.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.

Enhances graph classification models on small datasets.

Graph neural network predicts optimal coarse-grained mapping operators.

Study proves hyperfiniteness of mapping class group actions on surface graphs.

Study of mapping class groups of infinite graphs, focusing on their finiteness and commensurability.

Study shows pants graph automorphisms match mapping class groups of nonorientable surfaces.

The study examines translation lengths of pseudo-Anosov maps on curve graphs.

The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.

Parabolic mapping class acts on curve graphs of infinite type surfaces.

The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.

We show that an Anosov map has a geodesic axis on the curve graph of a torus. The direct corollary of our result is the stable translation length of an Anosov map on the curve graph is always a positive integer. As the proof is constructive, we also provide an algorithm to calculate the exact translation length for any…

Study of flip graphs and their automorphism groups for infinite-type surfaces.

Study of pure mapping class groups on infinite graphs.

Study of graphs from hexagon decompositions of surfaces.

In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher order generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-W…

Optimal Euclidean structure minimizes energy in weighted toroidal graphs.

Study uniformly differentiable graphs in Carnot groups, proving area formulas.

The study examines when mapping class groups are quasi-isometric to graphs of curves.

Study of endperiodic maps on infinite graphs, proving homotopy and eigenvalue properties.

3D manifolds can map to a plane with specific curve patterns.

Let $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components with $g \geq 2$, $n \geq 0$. Let $\mathcal{N}(R)$ be the nonseparating curve graph, $\mathcal{C}(R)$ be the curve graph and $\mathcal{HT}(R)$ be the Hatcher-Thurston graph of $R$. We prove that if $λ: \mathcal{N}(R) \rightarro…

We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.

Study shows surfaces without certain curves have infinite orbit graph.

New theory classifies knotted spheres in 4D space.

Groups of homotopy equivalences of graphs help realize compact subgroups.

Godin introduced the categories of open closed fat graphs $Fat^{oc}$ and admissible fat graphs $Fat^{ad}$ as models of the mapping class group of open closed cobordism. We use the contractibility of the arc complex to give a new proof of Godin's result that $Fat^{ad}$ is a model of the mapping class group of open-close…

We consider the mean curvature flow of the graph of a smooth map $f:\mathbb{R}^2\to\mathbb{R}^2$ between two-dimensional Euclidean spaces. If $f$ satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays the graph of an area-decreasing map $f_t$. Further, we prove unifo…

We construct maps on hat Heegaard Floer homology for cobordisms decorated with graphs. The graph TQFT allows for cobordisms with disconnected ends. Our construction uses Juhász's sutured Floer TQFT. We compute the maps for several elementary graph cobordisms. As an application, we compute the action of the fundamental …

WEGL embeds graphs in a vector space for faster machine learning.

The period mapping assigns to each rank n, marked metric graph Gamma a positive definite quadratic form on H_1(Gamma). This defines maps Phi* and Phi on Culler--Vogtmann's outer space CV_n, and its Torelli space quotient T_n, respectively. The map Phi is a free group analog of the classical period mapping that sends a …

For given closed orientable 3-manifolds $M$ and $N$ let $cD(M,N)$ be the set of mapping degrees from $M$ to $N$. We address the problem: For which $N$, $cD(M,N)$ is finite for all $M$? The answer is known in Thurston's picture of closed orientable irreducible 3-manifolds unless the target is a non-trivial graph manifol…

Researchers prove the automorphism group of a sphere complex matches the mapping group of a graph.

Theta graph diffeomorphism shows nontrivial mapping class of 4-sphere.

Paper estimates Gaussian curvature of minimal graphs in a specific manifold.

Study measures complexity of surfaces using a new graph to prove group properties.

Random projections help in representing sparse graphs efficiently.

The paper studies mapping class groups of locally finite graphs and their associated sphere complexes.

In this paper we study some consequences of the author's classification of graph manifolds by their profinite fundamental groups. In particular we study commensurability, the behaviour of knots, and relation to mapping classes. We prove that the exteriors of graph knots are distinguished among all 3-manifold groups by …

Automorphisms of fine curve graph match surface homeomorphisms.

DHGAK aligns substructures for better graph kernel performance.

The study explores normal generators for mapping class groups and their properties.