Related papers: A partial order on multibranched surfaces in 3-man…

A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…

In this paper, we give a lower bound for the maximum and minimum genus of a multibranched surface by the first Betti number and the minimum and maximum genus of the boundary of the neighborhood of it, respectively. As its application, we…

We give an elementary proof of the fact that any orientable 3-manifold admits a framing (i.e. is parallelizable) and any non-orientable 3-manifold admits a projective framing. The proof uses only basic facts about immersions of surfaces in…

We study the existence of geometrically controlled branched covering maps from $\mathbb R^3$ to open $3$-manifolds or to decomposition spaces $\mathbb S^3/G$, and from $\mathbb S^3/G$ to $\mathbb S^3$.

A collection of simple closed curves in $\rr^3$ is called a negative slice if it is the intersection of a flat-at-infinity planar Lagrangian surface and $\{y_2 = a \}$ for some $a < 0$. Examples and non-examples of negative slices are…

This paper initiates the study of circular orderability of $3$-manifold groups, motivated by the L-space conjecture. We show that a compact, connected, $\mathbb{P}^2$-irreducible $3$-manifold has a circularly orderable fundamental group if…

We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or Enriques surface to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big…

In this paper, we give an algorithm to build all compact orientable atoroidal Haken 3-manifolds with tori boundary or closed orientable Haken 3-manifolds, so that in both cases, there are embedded closed orientable separating incompressible…

We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.

This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a…

The surface states of a symmetry protected topological state can have many possibilities. Here we propose a chiral Abelian topological order on a distinct surface of a multilayer-stacked cluster Mott insulating system. The first-principle…

We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.

This is a preliminary note on a family of minimal surfaces in the 3-sphere defined by a compatible fourth order equation. The minimal surfaces are geometrically characterized either by having a surface of revolution like induced metric, or…

It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…

A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…

We consider the problem of when a closed hyperbolic surface admits a totally geodesic embedding into a closed hyperbolic 3-manifold, and in particular equivariant versions of such embeddings. In a previous paper we considered…

Let $k$ be a number field and $B$ be a central simple algebra over $k$ of dimension $p^2$ where $p$ is prime. In the case that $p=2$ we assume that $B$ is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

We say that a $2$-dimensional CW complex is a multibranched surface if we remove all points whose open neighborhoods are homeomorphic to the $2$-dimensional Euclidean space, then we obtain a $1$-dimensional complex which is homeomorphic to…

By work of Uhlenbeck, the largest principal curvature of any least area fiber of a hyperbolic $3$-manifold fibering over the circle is bounded below by one. We give a short argument to show that, along certain families of fibered hyperbolic…