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We study the vibrational spectrum of a constrained classical ring. Due to the presence of 2-order exceptional points, a topologically trivial band at the infinity can make the vibrational band topologically nontrivial. The symmetry, which…

We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems…

We consider holomorphic foliations by curves on compact complex manifolds, for which we investigate the existence of projective structures along the leaves varying holomorphically (foliated projective structures), that satisfy particular…

To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a…

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 this paper, we consider non developable ruled surface with spacelike ruling, timelike ruling, respectively. We give the relations between the structure functions with the curvature and torsion of the striction line of the timelike and…

Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference…

One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not…

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…

This paper, which is an outgrowth of a previous paper of the authors, continues the study of dimension 1 foliations on non-metrisable manifolds emphasising some anomalous behaviours. We exhibit surfaces with various extra properties like…

A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of…

We show that a torus knot which is not 2-bridge has a unique irreducible bridge splitting of positive genus.

We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable…

We show that for certain hyperbolic 3-manifolds, all boundary slopes are slopes of immersed incompressible surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…

In this paper, we develop a coarse analogue of treewidth. We prove that a graph $G$ admits a tree-decomposition in which each bag is contained in the union of a bounded number of balls of bounded radius, if and only if $G$ admits a…

Structural stability of piecewise M\"obius transformations (PMTs) is examined from various perspectives. A result concerning structural stability, restricted to the space of PMTs, is derived using hyperbolic characteristics of the component…

Given an irreducible, end-periodic homeomorphism f of a surface S with finitely many ends, all accumulated by genus, the mapping torus is the interior of a compact, irreducible, atoroidal 3-manifold with incompressible boundary. Our main…

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic…