Related papers: Detecting and visualizing 3-dimensional surgery

While three-dimensional imaging is essential for clinical diagnosis, its high cost and long wait times have motivated the use of image-to-3D foundation models to infer volume from two-dimensional modalities. However, because these models…

Analysis of three-dimensional biological samples is critical to understanding tissue function and the mechanisms of disease. Many chronic conditions, like neurodegenerative diseases and cancers, correlate with complex tissue changes that…

Let K be a non-trivial knot in the 3-sphere and let Y be the 3-manifold obtained by surgery on K with surgery-coefficient 1. Using tools from gauge theory and symplectic topology, it is shown that the fundamental group of Y admits a…

When a toddler is presented a new toy, their instinctual behaviour is to pick it upand inspect it with their hand and eyes in tandem, clearly searching over its surface to properly understand what they are playing with. At any instance…

We define a graph encoding the structure of contact surgery on contact 3-manifolds and analyze its basic properties and some of its interesting subgraphs.

Small covers arising from 3-dimensional simple polytopes are an interesting class of 3-manifolds. The fundamental group is a rigid invariant for wide classes of 3-manifolds, particularly for orientable Haken manifolds, which include…

The crushing operation of Jaco and Rubinstein is a powerful technique in algorithmic 3-manifold topology: it enabled the first practical implementations of 3-sphere recognition and prime decomposition of orientable manifolds, and it plays a…

Tissue deformation in ultrasound (US) imaging leads to geometrical errors when measuring tissues due to the pressure exerted by probes. Such deformation has an even larger effect on 3D US volumes as the correct compounding is limited by the…

In this article, we define the contact surgery distance of two contact 3-manifolds $(M,\xi)$ and $(M',\xi')$ as the minimal number of contact surgeries needed to obtain $(M,\xi)$ from $(M',\xi')$. Our main result states that the contact…

In the singularity and differential topological theory of Morse functions and higher dimensional versions or fold maps and application to algebraic and differential topology of manifolds, constructing explicit fold maps and investigating…

Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…

Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…

This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known contructions for these sets on $2D$ manifolds of constant curvature (the…

Humans rely on their visual and tactile senses to develop a comprehensive 3D understanding of their physical environment. Recently, there has been a growing interest in exploring and manipulating objects using data-driven approaches that…

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

We provide infinitely many rational homology 3-spheres with weight-one fundamental groups which do not arise from Dehn surgery on knots in $S^3$. In contrast with previously known examples, our proofs do not require any gauge theory or…

Hyperbolic Dehn surgery and the bending procedure provide two ways which can be used to describe hyperbolic deformations of a complete hyperbolic structure on a 3-manifold. Moreover, one can obtain examples of non-Haken manifolds without…

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as…

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

We study a notion of strict pseudoconvexity in the context of topologically (often unsmoothably) embedded 3-manifolds in complex surfaces. Topologically pseudoconvex (TPC) 3-manifolds behave similarly to their smooth analogues, cutting out…