Related papers: On the order of Dehn twists

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

The purpose of this paper is to give a complete description of the Cohn localization of the augmentation map $Z[G]\rightarrow Z$ when $G$ is any finite group.

This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new…

The mapping class group of an orientable surface, which records its symmetries up to isotopy, plays a central role in low-dimensional topology. This chapter explores the foundational problem of determining minimal generating sets for these…

The goal of this article is to survey recent developments in the theory of contact structures in dimension three.

Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski obtained an explicit finite presentation for the mapping class group $M(N_{g,s})$ of the surface $N_{g,s}$, where…

We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.

Let $C$ be a curve in a closed orientable surface $F$ of genus $g \geq 2$ that separates $F$ into subsurfaces $\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\Mod(F)$ of the Dehn twist $t_C$ about $C$. All…

Under consideration are the construction and properties of some special class of second other tangent sets on using the technique of nonstandard analysis.

The aim of this paper is to realise the techniques of picture-valued invariants and invariants valued in free groups for long knots in the full torus. Such knots and links are of a particular interest because of their relation to Legendrian…

We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.

Knots obtained by Dehn filling the Whitehead sister link include some of the smallest volume twisted torus knots. Here, using results on A-polynomials of Dehn fillings, we give formulas to compute the A-polynomials of these knots. Our…

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted…

We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.

Given a morphism $X \to S$ of fine log schemes, we develop a geometric description of the sheaves of higher-order differentials $\Omega^n_{X/S}$ for $n > 1$, as well as a definition of the de Rham complex in terms of this description.

This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.

We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian varieties.

This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.

We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four…

We give a more coherent definition of upward planar order.