Results 51 to 60 of about 707 (188)
Persistent entropy for separating topological features from noise in vietoris-rips complexes [PDF]
Journal of Intelligent Information Systems, 2017 Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such sequence is called the persistence barcode. k-Dimensional holes with short lifetimes are informally considered to be
Nieves Atienza +2 more
openaire +4 more sources
Infinity‐operadic foundations for embedding calculus
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract Motivated by applications to spaces of embeddings and automorphisms of manifolds, we consider a tower of ∞$\infty$‐categories of truncated right modules over a unital ∞$\infty$‐operad O$\mathcal {O}$. We study monoidality and naturality properties of this tower, identify its layers, describe the difference between the towers as O$\mathcal {O}$
Manuel Krannich, Alexander Kupers
wiley +1 more source
Thurston norm for coherent right‐angled Artin groups via L2$L^2$‐invariants
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract We define a new notion of splitting complexity for a group G$G$ along a non‐trivial integral character ϕ∈H1(G;Z)$\phi \in H^1(G; \mathbb {Z})$. If G$G$ is a one‐ended coherent right‐angled Artin group, we show that the splitting complexity along an epimorphism ϕ:G→Z$\phi \colon G \rightarrow \mathbb {Z}$ equals the L2$L^2$‐Euler characteristic
Monika Kudlinska
wiley +1 more source
About $wcs$-covers and $wcs^*$-networks on the Vietoris hyperspace $\mathcal F(X)$
, 2023 summary:We study some generalized metric properties on the hyperspace $\mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. We prove that $X$ has a point-star network consisting of (countable) $wcs$-covers if and only if so
Tuan, Phan D. +3 more
core +1 more source
A short note on hit-and-miss hyperspaces
Applied General Topology, 2003 Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “κ-Lindelöfness” and “κ-compactness” for cardinals κ.
René Bartsch, Harry Poppe
doaj +1 more source
On virtual chirality of 3‐manifolds
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract We prove that if a prime 3‐manifold M$M$ is not finitely covered by the 3‐sphere or a product manifold, then M$M$ is virtually chiral, that is, it has a finite cover that does not admit an orientation‐reversing self‐homeomorphism. In general, if a 3‐manifold contains a virtually chiral prime summand, then it is virtually chiral.
Hongbin Sun, Zhongzi Wang
wiley +1 more source
Relationship among various Vietoris-type and microsimplicial homology theories [PDF]
, 2021 summary:In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T.
Imamura, Takuma
core +1 more source
Graphical small cancellation and hyperfiniteness of boundary actions
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned‐off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented) classical small cancellation groups, admit hyperfinite boundary actions, more precisely, the orbit equivalence ...
Chris Karpinski +2 more
wiley +1 more source
Ecology Letters, Volume 29, Issue 2, February 2026.We use topological data analysis to reveal a persistent morphological gap in a major group of songbirds (superfamily Passeroidea). The gap remained unoccupied for millions of years, even though nearby morphologies are common and the same body form exists in other groups of birds.
Stephanie Y. Chia +4 more
wiley +1 more source
Applied General Topology, 2003 Recently it was shown that, in a metric space, the upper Wijsman convergence can be topologized with the introduction of a new far-miss topology. The resulting Wijsman topology is a mixture of the ball topology and the proximal ball topology.
Giuseppe Di Maio +2 more
doaj +1 more source