Related papers: Representing Fields without Correspondences: the L…

We present a simple way of constructing conformal couplings of a scalar field to higher order Euler densities. This is done by constructing a four-rank tensor involving the curvature and derivatives of the field, which transforms…

In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations, weakening the…

The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…

This paper introduces effectful toposes as an extension of the effective topos and investigates their structure relative to Lawvere-Tierney topologies. First, we formulate effectful toposes by lifting the evidenced frame, which is a…

A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we present a bijective link between unicellular maps on a non-orientable surface and…

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…

The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the Local Euler Characteristic Transform ($\ell$-ECT), a novel…

This paper is an introductory and informal exposition on the topology of polygonal meshes. We begin with a broad overview of topological notions and discuss how homeomorphisms, homotopy, and homology can be used to characterise topology. We…

Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.

Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…

We discuss the topological properties of the manifold of coupling constants for multi-coupling deformations of conformal field theories. We calculate the Euler and Betti numbers and briefly discuss physical applications of these results.

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Template 3D shapes are useful for many tasks in graphics and vision, including fitting observation data, analyzing shape collections, and transferring shape attributes. Because of the variety of geometry and topology of real-world shapes,…

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…

A coupling between the spacetime geometry and a scalar field involving the Euler four-form can have important consequences in General Relativity. The coupling is a four-dimensional version of the Jackiw-Teitelboim action, in which a scalar…

We consider the Euler type integral associated to the configuration space of points on an elliptic curve, which is an analogue of the hypergeometric function associated to the configuration space of points on a projective line. We calculate…