arXiv research

New method preserves topology in Hodge decomposition for scalar and vector fields.

IVFS simplifies feature selection for high-dimensional data preservation.

Reproduces IVFS for high-dimensional data structure preservation.

Topologically and geometrically engaging actions have proved to be useful to obtain rigidity results for semisimple Lie group actions. We show that the action of a simple noncompact Lie group on a compact manifold preserving a unimodular rigid geometric structure of algebraic type (e.g. a connection together with a vol…

Study reveals failure of uniqueness in dynamical invariants for 3D volume-preserving diffeomorphisms.

New method reduces spatial graphs while preserving their topological features.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theo…

Pluriclosed flow preserves Hermitian-symplectic structures and forms, with topological constraints.

Paper proposes G-CRD to improve GNNs by preserving global graph topology.

An algorithm preserves topological features in dimensionality reduction.

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.

The study explores how different Grothendieck topologies and functors between categories preserve locality.

Dunkl connections on complex plane don't preserve metrics.

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 $S^3$.

Regularization preserves topological data structure in autoencoders.

DMT enhances deep neural networks to better preserve data structures.

We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in $S^3$.

This paper determines all possible topological symmetry groups of generalized Petersen graphs.

We show that except for $n = 2$ if a bridge surface for a knot is an index $n$ topologically minimal surface, then after a perturbation it is still topologically minimal with index at most $n+1$.

CycleMorph improves image registration by preserving topology with cycle consistency.

Improved retinal vessel segmentation with topology preservation trade-off.

We prove that graph products constructed over infinite graphs with bounded clique number preserve finite asymptotic dimension. We also study the extent to which Dranishnikov's property C, and Dranishnikov and Zarichnyi's straight finite decomposition complexity are preserved by constructions such as unions, free produc…

Various standard texts on differential topology maintain that the level-preserving map defined by the track of an isotopy of embeddings is itself an embedding. This note describes a simple counterexample to this assertion.

Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i - the combinatorics is preserved, and ii- the boundary is preserved: vertices corres…

FibeRed reduces complex data dimensions while preserving topology.

Paper tackles few-shot class-incremental learning with a neural gas network.

Enhances graph embeddings by preserving graph topology.

We show that every volume preserving codimension one Anosov flow on a closed Riemannian manifold of dimension greater than three admits a global cross section and is therefore topologically conjugate to a suspension of a linear toral automorphism. This proves a conjecture of Verjovsky from the 1970's in the volume pres…

Curvature regularization prevents distortion in graph embeddings.

Paper classifies pillow box isometric deformations preserving crease patterns.

Smooth isotopy on cube saves energy with extra dimensions.

CMS formulation solves Poincare conjecture for all dimensions.

Curvature of 2D subsets preserved in their space.

Finite rigid sets found in surface curve complexes.

We study the long time behavior of the volume preserving $p$-flow in $\mathbb{R}^{n+1}$ for $1\leq p<\frac{n+1}{n-1}$. By extending Andrews' technique for the flow along the affine normal, we prove that every centrally symmetric solution to the volume preserving $p$-flow converges sequentially to the unit ball in the $…

This paper is first-line research expanding GANs into graph topology analysis. By leveraging the hierarchical connectivity structure of a graph, we have demonstrated that generative adversarial networks (GANs) can successfully capture topological features of any arbitrary graph, and rank edge sets by different stages a…

In this paper we study the topology of pseudo convex CR manifolds whose Reeb flow preserves the Levi metric.

In this paper we initiate a study of the topological group $PPQI(G,H)$ of pattern-preserving quasi-isometries for $G$ a hyperbolic Poincare duality group and $H$ an infinite quasiconvex subgroup of infinite index in $G$. Suppose $\partial G$ admits a visual metric $d$ with $dim_H < dim_t +2$, where $dim_H$ is the Hausd…

We study the area preserving Willmore flow in an asymptotic region of an asymptotically flat manifold which is $C^{3}-$close to Schwarzschild. It was shown by Lamm, Metzger and Schulze that such an end is foliated by spheres of Willmore type. In this paper, we prove that the leaves of this foliation are stable under sm…

In this paper, we consider a new length preserving curve flow for convex curves in the plane. We show that the global flow exists, the area of the region bounded by the evolving curve is increasing, and the evolving curve converges to the circle in C-infinity topology as t goes to infinity.

In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non finite…

Suppose M is a noncompact connected 2-manifold and m is a good Radon measure of M with m(partial M) = 0. Let H(M)_0 denote the identity component of the group of homeomorphisms of M equipped with the compact-open topology and let H(M; m)_0 denote the identity component of the subgroup consisting of m-preserving homeomo…

We study groups of circle diffeomorphisms whose action on the cylinder $\mathcal C=\mathbb S^1\times \mathbb S^1\setminus Δ$ preserves a volume form. We first show that such a group is topologically conjugate to a subgroup of $\rm{PSL}(2,\mathbb R)$, then discuss the existence of a differentiable conjugacy.

The study connects electromagnetic structures to Legendrian fields on the 3-sphere.

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…

The paper studies totally nonnegative parts of flag varieties and their topologies.

Study on symplectic structures and their deformations.

In this paper we construct effective invariants for braid monodromy of affine curves. We also prove that, for some curves, braid monodromy determines their topology. We apply this result to find a pair of curves with conjugate equations in a number field but which do not admit any orientation-preserving homeomorphism.