arXiv research

We extend Howie's characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary and sufficient conditions for a knot to be toroidally alternating. We also give a topological characterization of almost-alternating knots whi…

This note characterizes monohedral tilings of regular polygons with up to three tiles.

3-manifold triangulations are Golod and tight, proven through a topological characterization.

We introduce the continuum self-similar tree (CSST) and characterize it topologically. We apply this to answer a question of Curien about the topology of the continuum random tree (CRT). We also give a topological characterization of other trees with branch points of finite or infinite valences.

Characterizes curves with short representatives on hyperbolic surfaces.

Generalizing Howie and Greene's characterization of alternating knots, we give a topological characterization of almost alternating knots.

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias.…

We present and prove a topological characterization of geodesic laminations on hyperbolic surfaces of finite type.

New characterizations for manifolds with boundary rigidity results.

Study topological properties of foliations induced by closed 1-forms on orbifolds.

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.

Characterizes continuity of monotone functionals in mixed topology.

New link topology connects permutation discrepancies to Diaconis-Graham inequalities.

For each $n\leq 6$, we characterize all the groups which can occur as either the orientation preserving topological symmetry group or the topological symmetry group of some embedding of $K_n$ in $S^3$.

Study characterizes compact Einstein-type manifolds with boundary.

Study of profinite quandles with constructions and characterizations.

The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with…

Characterizes Anosov flows in 3D using symplectic and contact geometry.

Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological manifolds in dimensions $5$, $6$, and $7$ and obtain topological characterizations…

Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…

Characterizes quasiconformally homogeneous ladder surfaces.

This paper characterizes stable polynomial mappings in a specific set.

Characterizes multitwists in surface mapping class groups.

In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its topological symmetry group.

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of the complete graph K_{4r+3} in S^3.

New proofs of h-principles in contact 3-manifolds.

Characterizes alternating links in thickened surfaces using Gordon-Litherland pairing.

Distance function to a finite set is a topological Morse function.

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be more intuitive and geometric. This is to be done over the field of complex numbe…

The paper characterizes and contrasts knots with high 4D clasp numbers.

The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-si…

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are su…

Characterizes isolated compact subgroups in Lie groups.

We characterize functions which are growth types of Riemannian manifolds of bounded geometry.

We prove that any rigid representation of $π_1Σ_g$ in $\mathrm{Homeo}_+(S^1)$ with Euler number at least $g$ is necessarily semi-conjugate to a discrete, faithful representation into $\mathrm{PSL}(2,\mathbb{R})$. Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions by a topological rig…

Novel tRSA combines geometry and topology for brain and model analysis.

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property)…

We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a number of known results. New results include a combinatorial characterization of c…

Study topological hyperbolicity of moduli spaces of elliptic surfaces.

This work characterizes topological descriptors of graph products and their expressive power.

Extends topological results for nonpositive curvature spaces.

New compactification for character varieties with good topological properties.

In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that 2-dimensional topological field theories (over a point) are described by finite-dim…

Finite-type surfaces have a topological Hopf property.

Proposes a probabilistic framework for stationary topological signals on simplicial complexes.

The paper characterizes limits of manifolds using Gromov-Hausdorff metric.

Study on the topology of leaves in singular Riemannian foliations.