Critiques incorrect fixed point assertions in digital topology.
problem Incorrect or incorrectly proven fixed point assertions in digital topology.
method Critical review of existing assertions.
result Identifies and critiques incorrect fixed point assertions.
Incorrect fixed point results in digital topology are debunked.
problem Incorrect fixed point results in digital topology.
method Mimicking classical topology tools.
result Many recent fixed point results are incorrect or trivial.
The paper highlights issues in fixed point claims in digital topology.
problem Flaws in published assertions about fixed points in digital metric spaces.
method Continues a series of studies examining these flaws.
result Identifies and discusses problems in fixed point claims.
Incorrect fixed point results in digital topology are corrected.
problem Incorrect fixed point results in digital topology.
method Analysis of recent papers in digital topology.
result Corrected incorrect conclusions in fixed point results.
Corrects incorrect assertions about fixed points in digital topology.
problem Incorrect or incorrectly proven assertions about fixed points in digital metric spaces.
method Analysis of existing assertions and proofs.
result Identifies and corrects errors in published assertions.
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect or poorly stated fixed point assertions in digital topology.
method Discussion of problematic publications in digital metric spaces.
result Clarification of incorrect fixed point assertions.
Fixed point assertions in digital topology are often incorrect or poorly stated.
problem Fixed points in digital metric spaces
method Discussing publications with bad assertions
result Identifying and correcting errors in fixed point assertions
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect, incorrectly proven, or trivial fixed point assertions in digital topology.
method Continues earlier work on identifying and critiquing bad fixed point assertions.
result Clarifies the nature and extent of incorrect fixed point assertions in digital topology.
The paper highlights issues with fixed point claims in digital images.
problem Flaws in published assertions about fixed points in digital images.
method Continues a series of studies examining digital topology.
result Identifies and discusses problems with fixed point claims.
The paper addresses flaws in fixed point assertions for digital images.
problem Deficiencies in previously published works on fixed point assertions for digital images.
method Continues a series of studies to identify and rectify issues in fixed point assertions.
result Identifies and corrects flaws in fixed point assertions for digital images.
The paper corrects and improves previous assertions in digital topology.
problem Incorrect or insufficiently proven assertions in digital topology.
method Review and correction of existing assertions.
result Improved and corrected assertions in digital topology.
New proofs in fixed point theory for manifolds and domains.
problem Proving fixed points and isometries for specific geometric structures.
method Topological fixed point theory applied to manifolds and domains.
result Prime divisors of finite group orders are constrained by domain connectivity.
Study fixed points in digital images, introducing new invariants.
problem Understanding properties of digital images through fixed points.
method Introduce new invariants and freezing/cold sets to analyze fixed point sets.
result Existence of fixed point sets restricts maps on their complements.
The paper corrects and improves previous assertions in digital topology.
problem Incorrect or poorly proven assertions in digital topology.
method Review and correction of existing assertions.
result Improved and corrected assertions in digital topology.
New tools for constructing fixed point sets in digital topology.
problem Constructing fixed point sets in digital topology.
method Defining excludable points and articulation points, and showing their exclusion from freezing sets.
result Excludable points and articulation points can be excluded from all freezing sets.
The paper studies Morse flows on 3-manifold boundaries with fixed points.
problem Classifying Morse flows on 3-manifold boundaries.
method Constructing a Pr-diagram as a topological invariant.
result A complete topological invariant of Morse flows on 3-manifold boundaries.
Surface groups found in interval diffeomorphisms without global fix points.
problem Existence of surface groups in interval diffeomorphisms.
method Analyzing the structure of diffeomorphisms of the interval.
result Surface groups with specific properties in interval diffeomorphisms.
Digital trees have approximate fixed point property, and conditions for products are explored.
problem Conditions for the approximate fixed point property in digital tree products.
method Analyzes digital trees and their products, explores conditions for the AFPP.
result Conditions are found for the AFPP in digital tree products.
This research classifies singular foliations and finds a universal deformation.
problem Classifying singular foliations on (C2,0). method Topological universal deformation through fixed invariants.
result Every equisingular deformation uniquely factors through the topological universal deformation.
The paper explores properties of continuous actions on manifolds, proving bounds on subgroup size and fixed points.
problem Properties of continuous finite group actions on topological manifolds.
method Analyzes properties including Jordan property and almost fixed point property, proving bounds on subgroup size.
result Existence of a constant C such that for any continuous action of a finite group G on a manifold X, there is a subgroup H with [G:H] ≤ C and a fixed point.
The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation…
The paper proves metrizability and dynamics of Weil bundles.
problem Metrizability and dynamics of Weil bundles in differential geometry.
method Investigation of metrizability and dynamics of Weil bundles for smooth compact manifolds and Weil algebras.
result A canonical, complete, weighted metric \(\mathfrak{d}_w\) on \(M^\mathbf{A}\) that encodes geometry and deformations.
New algorithm for collaborative deep learning over fixed networks.
problem Data parallelization and decentralized computation in deep learning.
method Consensus-based distributed SGD (CDSGD) and CDMSGD algorithms for fixed topology networks.
result Demonstrated improved performance over centralized and federated learning algorithms.
We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most pi/2, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are su…
Small entropy self-expanders are topologically unique.
problem Uniqueness of self-expanders with small entropy.
method Analysis of mean curvature flow and cone asymptotics.
result All solutions are in the same isotopy class.
The study examines the flexibility of entropies for negatively curved surfaces.
problem The study investigates the flexibility of topological and metric entropies for negatively curved surfaces.
method The authors compare different metrics on surfaces of negative curvature and analyze their topological and metric entropies.
result The study proves that the topological and metric entropies for metrics of negative curvature are flexible and only equal in the case of constant negative curvature.
Study of loop braid groups for 3D manifolds, linking algebra and dynamics.
problem Lack of a 3D framework for braid group theory in topological dynamics.
method Introduce loop braid groups and associate Burau matrix representations with generalized Lefschetz number.
result Established a connection between loop braid groups and topological dynamical properties, providing estimates for periodic points.
We survey work on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with boundary. The interior of AH(M) is quite well-understood, but the topology of the entire space can be quite complicated. However, the topology is well-behaved at many points …
Groups with certain actions on CAT(0) spaces have global fixed points.
problem Understanding group actions on CAT(0) spaces with fixed points.
method Criterion for group elements to have fixed points in semi-simple actions on finite-dimensional CAT(0) spaces.
result Thompson's group T and related groups have global fixed points in specific CAT(0) spaces.
The paper classifies involutions on S^4, proving linearities under certain conditions.
problem Classifying involutions on S^4 with specific fixed-point sets.
method Combining surgery theory, Schoenflies theorem, and equivariant topology.
result Linear involutions on S^4 with 1-dimensional fixed-point sets are proven.
Study shows certain surface homeomorphisms groups can't be precompact.
problem Understanding precompactness of groups of surface homeomorphisms.
method Analyzing subgroup properties and transitivity of homeomorphisms.
result No subgroup of surface homeomorphisms can be Roelcke precompact.
We construct infinite sequences of pseudo-Anosov homeomorphisms without fixed points and leaving invariant a sequence of orientable measured foliations on the same topological surface and the same stratum of the space of abelian differentials. The existence of such sequences show that all pseudo-Anosov homeomorphisms f…
Study torus orbifolds with two fixed points and their cohomology.
problem Understanding the topological and cohomological properties of torus orbifolds with two fixed points.
method Analyze the equivariant topological type and use results from [DKS] to compute integral equivariant cohomology.
result Results on generators and relations for the cohomology of torus orbifolds with two fixed points.
For fixed large genus, we construct families of complete immersed minimal surfaces in R3 with four ends and dihedral symmetries. The families exist for all large genus and at an appropriate scale degenerate to the plane.
Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.
problem Analyzing the growth of derivative maxima for C2 interval diffeomorphisms with parabolic fixed points. method Examining C2 diffeomorphisms with only parabolic fixed points, focusing on tangency and repelling behavior. result Maximal growth of derivative maxima is exactly quadratic for diffeomorphisms with a non-quadratic tangency to identity at a repelling fixed point.
The paper studies co-Hamiltonian diffeomorphisms on compact cosymplectic manifolds.
problem Fix-point theory and co-Hamiltonian diffeomorphisms on compact cosymplectic manifolds.
method Fix-point theory, Arnold's conjecture, co-Hofer norms, topologies, approximations lemmas.
result Minimum number of fix points for co-Hamiltonian diffeomorphisms is at least 1.
M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and som…
Formula estimates pseudo-Anosov maps' fixed points, linking to surface properties.
problem Estimating fixed points of pseudo-Anosov maps.
method Formula using Teichmüller translation length for fixed points of strong irreducible maps.
result Log of fixed points coarsely equals Teichmüller translation length for strong irreducible maps.
We study topological T-duality for spaces with a semi-free S1−action with isolated fixed points. Physically, these correspond to spacetimes containing Kaluza-Klein monopoles. We demonstrate that the physical dyonic coordinate of such spaces has an analogue in our formalism. By analogy with the Dirac monopole, we stu…
The paper studies contact topology submanifolds and their rigidity.
problem Contact topology submanifolds rigidity and degeneracy.
method Contact coisotropic submanifolds, pseudo-metric, Chekanov type pseudo-metric.
result A contact topology analogue to Chekanov's dichotomy of degeneracy.
New estimators show consistent estimation is possible with randomized item assignment.
problem Estimating underlying comparison probabilities from noisy pairwise comparisons.
method Study permutation-based models under strong stochastic transitivity, randomized item assignment.
result Rates of estimators are optimal for a large class of graphs.
Study geometric flows with varying parameters and prove continuous dependence.
problem Continuous dependence of flows on parameters in geometric settings.
method Derived suitable topologies for vector fields and flows, proved new continuous dependence.
result Proved continuous dependence of flows on parameters in a general topological space.
We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group Γ on a topological manifold where the fixed sets for any element are contained in codimension two submanifolds, every orbit e…
Perelman's Ricci flow emerges in quantum gravity, linking math and physics.
problem Understanding Perelman's Ricci flow equations in quantum gravity.
method Mapping Perelman's Ricci flow equations to localization equations in topological quantum gravity.
result Perelman's dilaton and fixed volume condition emerge dynamically.
Moduli spaces of semi-stable real and quaternionic vector bundles of a fixed topological type admit a presentation as Lagrangian quotients, and can be embedded into the symplectic quotient corresponding to the moduli variety of semi-stable holomorphic vector bundles of fixed rank and degree on a smooth complex projecti…
We study topological open string amplitudes on orientifolds without fixed planes. We determine the contributions of the untwisted and twisted sectors as well as the BPS structure of the amplitudes. We illustrate our general results in various examples involving D-branes in toric orientifolds. We perform the computation…
We announce the following result and give several applications: A Hamiltonian T-space (for T a torus) with isolated fixed points is cobordant to a disjoint union of weighted projective spaces which are constructed from its fixed point data. The applications concern the Duistermaat-Heckman formula, the topological J…