arXiv research

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite mutation sequences. We show transitivity of infinite mutation sequences on tria…

Book explores infinite translation surfaces, challenging traditional geometry.

Countable modular groups found on surfaces with infinite type.

Infinite-genus surfaces have many isospectral hyperbolic structures.

Study Euler class of surface bundles with nontrivial results.

Study flip graphs for surfaces of infinite type, finding uncountably many connected components.

Study infinite genus surfaces and Schottky groups for uniformization.

Overview of infinite surface mapping class groups.

The paper solves curvature problems on infinite hyperbolic surfaces.

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter a…

Simplified presentations for non-orientable surface mapping class groups.

Study on infinite energy maps from surfaces to CAT(0) spaces.

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

Paper constructs an infinite 3-7 surface in 3D space.

Infinite type surfaces can be perfectly divided into triangles.

Generates special homeomorphisms for complex surfaces.

The paper defines infinite Schottky groups and their applications to infinite type surfaces.

Criterion found for Teichmüller extremal maps on infinite Riemann surfaces.

Short proof shows infinite diameter for surface diffeomorphisms.

New method to parametrize infinite Riemann surfaces with bounded triangulations.

The paper provides infinite presentations for surface groups.

New rays on infinite type surfaces help understand their boundaries.

The paper constructs infinitely many surfaces with specific mean curvature.

In this paper, for a non compact and orientable surface $S$ been either: the Infinite Loch Ness monster, the Cantor tree and the Blooming Cantor tree, we construct explicitly an infinitely generated Fuchsian group $Γ<PSL(2,\mathbb{R})$, such that the quotient $\mathbb{H}/Γ$ is a hyperbolic surface homeomorphic to $S$.

Study mapping class groups of infinite type surfaces with noncompact boundaries.

This article presents some methods to control the bottom of the spectrum of the Laplacian $λ_0$ on hyperbolic surfaces with infinite volume. Our first result bounds the $λ_0$ of a geometrically finite surface in terms of the geometry of its convex core. We then focus on infinite type periodic hyperbolic surfaces built …

Study infinite symplectic forms on ruled surfaces.

Study surfaces in 4-manifolds with cyclic fundamental group.

The paper finds pseudo-Anosov-like maps on an infinite ladder surface.

The study characterizes infinite Riemann surfaces and their foliations using quadratic differentials.

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

New infinite-type loxodromic elements found in surface mapping classes.

The paper finds infinite knots with surfaces of any positive genus.

Study of infinite type surfaces' mapping class groups via hyperbolic structures.

Two results on end spaces of infinite type surfaces, answering questions about their topology and equivalence.

We study geodesics on a planar Riemann surface of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these geodesics and relate them to the structure of the boundary of a Dirichlet polygon for…

This paper provides an infinite presentation for a subgroup of mapping class groups of non-orientable surfaces.

Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.

Study shows density of mapping classes on infinite-type surfaces using quasi-conformal maps.

New surfaces show horocyclic flow isn't always minimal.

We show that a knot in $S^3$ with an infinite number of distinct incompressible Seifert surfaces contains a closed incompressible surface in its complement.

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

New Riemann surfaces with unique end and infinite type are constructed.

Study of CB generating sets for infinite-type surfaces.

Study on mapping class groups of infinite type surfaces.

The Loch Ness Monster admits many regular dessins d'enfants and different holomorphic structures.

The random graph is an infinite graph with the universal property that any embedding of $G-v$ extends to an embedding of $G$, for any finite graph. In this paper we show that this graph embeds in the curve graph of a surface $Σ$ if and only if $Σ$ has infinite genus, showing that the curve system on an infinite genus s…

Study finds infinitely many surface bundle types with zero signature.