Hacker News with Generative AI: Topology

Foams Made Out of Felt (tanyakhovanova.com)
A foam is a finite 2-dimensional CW-complex with extra properties. This one opening sentence is already more advanced than any of my usual blog posts. Let me define a finite 2-dimensional CW-complex in layman’s terms.
Mathematics, Topology, Art, Design
18 points by 082349872349872 2 days ago | 5 comments
A universal triangulation for flat tori (2022) (arxiv.org)
A result due to Burago and Zalgaller (1960, 1995) states that every orientable polyhedral surface, one that is obtained by gluing Euclidean polygons, has an isometric piecewise linear (PL) embedding into Euclidean space $\mathbb{E}^3$. A flat torus, resulting from the identification of the opposite sides of a Euclidean parallelogram, is a simple example of polyhedral surface. In a first part, we adapt the proof of Burago and Zalgaller, which is partially non-constructive, to produce PL isometric embeddings of flat tori. Our implementation produces embeddings with a huge number of vertices, moreover distinct for every flat torus. In a second part, based on another construction of Zalgaller (2000) and on recent works by Arnoux et al. (2021), we exhibit a universal triangulation with 2434 triangles which can be embedded linearly on each triangle in order to realize the metric of any flat torus.
Mathematics, Geometry, Topology
4 points by coley_moke 90 days ago | 1 comments
Real life example of a brunnian link (twitter.com)
Mathematics, Topology, Links
11 points by histories 126 days ago | 1 comments
The binding of cosmological structures by massless topological defects (academic.oup.com)
Cosmology, Physics, Topology
43 points by belter 178 days ago | 42 comments
Finite-Time Topology Identification of Delayed Complex Dynamical Networks (science.org)
Topology, Dynamical Systems, Networks, Complex Systems, Science
36 points by bryanrasmussen 178 days ago | 0 comments
Whitney Stratifications and Intersection Homology (2023) [pdf] (ethz.ch)
Mathematics, Topology, Research Papers
17 points by 082349872349872 180 days ago | 40 comments