相关论文: Manifolds admitting a continuous cancellative bina…

In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…

A complete list of irreducible triangulations is identified on the M\"obius band.

This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds $M$ that fiber over a non-orientable base space. An orientable base…

In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…

We study manifolds with almost nonnegative curvature operator (ANCO) and provide first examples of closed simply connected ANCO mannifolds that do not admit nonnegative curvature operator.

We show that a closed non-orientable $3$-manifold admits a positive scalar curvature metric if and only if its orientation double cover does; however, for each $4\le n\le 7$, there exist infinitely many smooth non-orientable $n$-manifolds…

We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the M\"obius band, and the products of a line with the total spaces of flat vector bundles over…

The boundary of a M\"obius manifold carries a canonical M\"obius structure. This enables one to define the cobordism group of $n$-dimensional (closed) M\"obius manifolds. The purpose of this note is to show that the cobordism group of…

In [AMW], it is proved that if a compact $3$-manifold has positive Ricci curvature and strictly convex boundary, then this manifold is diffeomorphic to the standard $3$-dimensional Euclidean disk. In this paper, we prove its…

Characterizations of binary operations between convex bodies on the Euclidean unit sphere are established. The main result shows that the convex hull is essentially the only non-trivial projection covariant operation between pairs of convex…

Let $M$ be a connected, closed, orientable, irreducible $3$-manifold. We show that: if $M$ admits a co-orientable taut foliation $\mathcal{F}$ with orderable cataclysm, then $\pi_1(M)$ is left orderable. This provides an elementary proof…

We prove that strictly mean convex toroids contain infinitely many (geometrically distinct) embedded free boundary minimal M\"obius bands as well as infinitely many embedded free boundary minimal annuli. The surfaces in both families are…

Various structural properties are developed for non-orientable surfaces in link spaces. The M\"obius band tree is described to represent genus growth of one-sided surfaces in solid tori. The structure of the Tree allows various insights…

It is shown that there exist $\mathcal{Z}$-compactifiable manifolds with noncompact boundary which fail to be pseudo-collarable.

Our objective is to illuminate the global structure of non-orientable manifolds with signature-changing metrics, with particular emphasis on global topological obstructions. Using explicit geometric constructions based on the topology of…

We prove that a closed $n$-manifold $M$ with positive scalar curvature and abelian fundamental group admits a finite covering $M'$ which is strongly inessential. The latter means that a classifying map $u:M'\to K(\pi_1(M'),1)$ can be…

Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.

A torus manifold $M$ is a $2n$-dimensional orientable manifold with an effective action of an $n$-dimensional torus such that $M^T\neq \emptyset$. In this paper we discuss the classification of torus manifolds which admit an invariant…

A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible,…

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…