Related papers: The excluded minors for embeddability into a compa…

For any m > 0, we construct properly embedded minimal surfaces in H^2 x R with genus zero, infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable number of limit ends. All these examples…

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $\mathcal{M}_{\sigma}$ of a compact closed surface $X$ of genus $\sigma$ is considered. A complete method of enumeration is achieved for…

The ends of a complete embedded minimal surface of {\em finite total curvature} are well understood (every such end is asymptotic to a catenoid or to a plane). We give a similar characterization for a large class of ends of {\em infinite…

We generalize the notion of graph minors to all (finite) simplicial complexes. For every two simplicial complexes H and K and every nonnegative integer m, we prove that if H is a minor of K then the non vanishing of Van Kampen's obstruction…

Mayhew et al.\ (2021) posed the problem of showing that the minor-closed class of spikes and their minors has a finite set of excluded minors and describing all of them. In this paper, we resolve this problem.

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when the surface is nonorientable.

A minimal family of curves on an embedded surface is defined as a 1-dimensional family of rational curves of minimal degree, which cover the surface. We classify such minimal families using constructive methods. This allows us to compute…

Huynh et al. recently showed that a countable graph $G$ which contains every countable planar graph as a subgraph must contain arbitrarily large finite complete graphs as topological minors, and an infinite complete graph as a minor. We…

We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…

Surfaces of finite geometric type are complete, immersed into the tree-dimensional Euclidean space with finite total curvature and Gauss map extending to an oriented compact surface as a smooth branched covering map over the unit sphere of…

We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of…

We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…

We present conditions on the Ricci curvature for complete, oriented, minimal submanifolds of Euclidean space, as well as the standard unit sphere, when the Gauss maps are bounded embeddings.

Given graphs $G$ and $H$, we propose a method to implicitly enumerate topological-minor-embeddings of $H$ in $G$ using decision diagrams. We show a useful application of our method to enumerating subgraphs characterized by forbidden…

Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an $\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge is an…

Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph $G$, the circuits of its bicircular lift matroid $L(G)$ are the edge sets of those subgraphs of $G$ that contain at least two cycles, and…

We determine the groups of minimal order in which all groups of order n can embedded for 1 < n < 16. We further determine the order of a minimal group in which all groups or order n or less can be embedded, also for 1 < n < 16.