Proof of Hilbert-Smith Conjecture in 2D.
problem Hilbert-Smith Conjecture in 2D
method Proof in dimension two
result Proved Hilbert-Smith Conjecture in 2D
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48 results for “Hilbert-Smith Conjecture”
The paper characterizes arithmetic metrics in coarsely geometric settings.
problem Characterizing arithmetic metrics in coarsely geometric settings.
method Using coarse-geometric commensurators and under the Hilbert-Smith conjecture.
result Positive answer in general and unconditional for specific cases.
The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The motivation is work of Cernavskii (``Finite-to-one mappings of manifolds'',…
The Hilbert-Smith Conjecturemath.GT
The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The motivation is work of Cernavskii (``Finite-to-one mappings of manifolds'',…
Generalizes manifold results for Lie groups, proving equivariant homotopy type.
problem Hilbert-Smith conjecture for topological -manifolds.
method Generalization of previous results, verification of n-classifying spaces.
result Any Palais-proper topological -manifold has the equivariant homotopy type of a countable proper -CW complex.
Applying standard techniques from Toeplitz operator theory, we analyze the asymptotics of the Hilbert-Smith norms of the TQFT operators coming from isotopy classes of one dimensional oriented submanifolds on a closed oriented surface. We thereby obtain a Toeplitz operator interpretation and generalization of the asympt…
This note is purely expository. A subset N of the plane is affine ambient homogeneous if for each x,y in N there exists an affine transformation taking x to y and N to itself. The result of D. Repovs, E. V. Scepin and the author on such subsets is presented, together with discussion, corollaries and generalizations. At…
In this paper we initiate a study of the topological group of pattern-preserving quasi-isometries for a hyperbolic Poincare duality group and an infinite quasiconvex subgroup of infinite index in . Suppose admits a visual metric with , where is the Hausd…
We show that every locally compact group which acts faithfully on a connected three-manifold is a Lie group. By known reductions, it suffices to show that there is no faithful action of (the -adic integers) on a connected three-manifold. If acts faithfully on , we find an interesting…
Polyhedra volume conjecture supports Stoker conjecture weakly.
problem Proving the Stoker conjecture for polyhedra.
method Using an extension of Montcouquiol and Weiss' result on polyhedra angles as local coordinates.
result Volume Conjecture for polyhedra implies a weak version of the Stoker conjecture.
Survey on two non-Kähler geometry conjectures.
problem Constant holomorphic sectional curvature and Fino-Vezzoni conjectures in non-Kähler geometry.
method Survey and discussion of historical and recent developments.
result Discussion of conjectures without new results.
Numerical study confirms Brennan's conjecture for a counterexample to Thurston's conjecture.
problem Thurston's conjecture and Brennan's conjecture in planar domains.
method Numerical analysis of a specific counterexample to Thurston's conjecture.
result The counterexample does not contradict Brennan's conjecture.
The non-vanishing conjecture implies the abundance conjecture in certain cases.
problem Abundance conjecture in algebraic geometry.
method Proof of the abundance conjecture under specific conditions.
result The abundance conjecture holds in dimensions ≤ 5 when κ ≥ 0 and ν ≤ 1.
Proves Gromov's conjecture and answers Stoker's polyhedron conjecture.
problem Gromov's flat corner domination conjecture and Stoker's conjecture for convex polyhedra.
method Same techniques applied to prove conjectures.
result Proves Gromov's conjecture and answers Stoker's polyhedron conjecture.
This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincare Conjecture. The paper also gives two other algebraic conjectures; one is equi…
Paper discusses conjectures and proves some related inequalities.
problem Unified generalization of BW and DDVV inequalities.
method Unified discussion and proofs of conjectures.
result Proves Conjecture 2 and obtains a new upper bound for Conjecture 3.
Symmetry-breaking in three differential geometry conjectures.
problem Exploring the role of symmetry in three differential geometry conjectures.
method Examining the Carathéodory, Willmore, and Lawson Conjectures through the lens of symmetry in 3D space-forms.
result Symmetry is broken, and more general ambient metrics are considered, leading to the failure of the conjectures.
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particula…
Study proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.
problem Integrality structure of framed knots' quantum invariants.
method Explicit formulas of colored HOMFLY-PT invariants of torus knots, verified in a limit form for any framed knots.
result Proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.
New proof shows most thin knots satisfy Cabling Conjecture.
problem Cabling Conjecture for thin knots using Heegaard Floer homology.
method Heegaard Floer homology and immersed curves techniques.
result Almost all thin knots satisfy the Cabling Conjecture.
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which tog…
The study confirms a conjecture for a specific type of knot.
problem Determining the topology of essential surfaces in knot theory.
method Analyzing twisted, generalized Whitehead doubles of knots.
result Twisted, generalized Whitehead doubles satisfy the Slope and Strong Slope Conjectures.
Metric SYZ conjecture proved using non-archimedean geometry.
problem Proving the metric SYZ conjecture in large generality.
method Using non-archimedean geometry to support the conjecture.
result Metric SYZ conjecture can be proved in large generality.
Proves Simon's conjecture for 3-manifolds.
problem Simon's conjecture for 3-manifolds.
method Proof for 3-manifolds.
result Proved Simon's conjecture for 3-manifolds.
Paper confirms Chen's biharmonic conjecture for hypersurfaces in 5D.
problem Chen's conjecture on biharmonic submanifolds in Euclidean spaces.
method Analyzes hypersurfaces in \(\mathbb{R}^5\) for \(n=4\).
result Chen's conjecture is confirmed for hypersurfaces in \(\mathbb{R}^5\) when \(n=4\).
Proved Farrell-Jones conjecture for free-by-cyclic groups.
problem Proving the Farrell-Jones conjecture for a specific class of groups.
method Geometric methods for establishing the Farrell-Jones Conjecture.
result Proved the Farrell-Jones conjecture for free-by-cyclic groups.
Counterexample disproves recent Penrose conjecture variant.
problem A variant of the Penrose conjecture.
method Provided a counterexample.
result The conjectured variant of the Penrose inequality is false.
Proofs On Arnold Conjecturesmath.SG
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
Proof outlined for 4D smooth Poincaré conjecture.
problem 4-dimensional smooth Poincaré conjecture.
method Outline of proof.
result Proof of 4D smooth Poincaré conjecture.
In this paper, we generalize the Cosmetic Surgery Conjecture to an -cusped hyperbolic -manifold and prove it under the assumption of another well-known conjecture in number theory, so called the Zilber-Pink Conjecture. For and , we show them without the assumption.
The Novikov Conjecturemath.GT
Survey on Novikov conjecture and its applications.
problem Novikov conjecture in topology.
method Survey and recent developments.
result Applications to topological rigidity and non-rigidity.
Paper connects AJ conjecture and colored Jones polynomial potential function.
problem Relationship between -polynomial and colored Jones polynomial.
method Connects AJ conjecture and colored Jones polynomial potential function.
result Establishes connection between -polynomial and colored Jones polynomial potential function.
Akbulut and Kirby conjectured that two knots with the same -surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.
Counterexample disproves conjectures about log canonical thresholds.
problem Conjectures about log canonical thresholds were disproved.
method Provided a counterexample to both conjectures.
result Conjectures about log canonical thresholds are false.
Study confirms conjecture on Hermitian manifolds with bounded mass.
problem Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds with bounded mass.
method Analyzes conjecture using bounded mass property on compact Hermitian manifolds.
result Confirms Demailly-Păun and Tosatti-Weinkove's conjectures.
Reformulated Markov's conjecture in combinatorial terms.
problem Markov's uniqueness conjecture in integral necklaces.
method Geometric reformulation and combinatorial description.
result Explicitly described set of lengths on modular torus.
Paper confirms Whitehead's conjecture for aspherical 2-complexes.
problem Whitehead's conjecture about aspherical 2-complexes.
method Argument on ribbon sphere-links, generalized for aspherical 2-complexes.
result Whitehead's conjecture confirmed for aspherical 2-complexes.
We survey the recent results and current issues on the topological rigidity problem for closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. A number of open problems and conjectures are presented during the course of the discussion. We also review the status and app…
Verifies a conjecture for the figure eight knot.
problem Relates A-ideal and recurrence ideal of knots.
method Uses quantum A-ideals, q-holonomicity, and AJ conjecture.
result Strong AJ conjecture verified for figure eight knot.
Review of Yau's conjecture on zero sets of Laplace eigenfunctions.
problem Yau's conjecture on zero sets of Laplace eigenfunctions.
method Discussion of old and new results and methods related to the conjecture, including solutions and new results in smooth settings.
result Discussion of Donnelly and Fefferman's solution of the conjecture in the real-analytic Riemannian manifold case and new results in the smooth setting.
Fukaya-Yamaguchi conjecture holds in 4D manifolds with nonnegative curvature.
problem Fundamental group of nonnegative curvature manifolds.
method Observation in dimension 4.
result Fukaya-Yamaguchi conjecture holds in 4D.
Proved a combinatorial conjecture in machine learning.
problem None explicitly stated in the abstract.
method Binomial and multinomial sums identities.
result Proved a combinatorial conjecture.
In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this paper, we generalize Aubin's theorem and we prove the Hebey--Vaugon conjec…
There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove the genus 3 case, even in the absence of new progress on the generalized Propert…
Paper proves contractible fake surfaces up to complexity 6 are deformable.
problem Stable Andrews-Curtis conjecture and contractible fake surfaces.
method Induction scheme proving contractibility up to complexity 6.
result Contractible fake surfaces up to complexity 6 are 3-deformable.
Paper analyzes Bartnik's quasi-local mass conjectures and their validity.
problem Understanding the validity of Bartnik's quasi-local mass conjectures.
method Developed a framework to analyze Bartnik's static vacuum extension conjecture.
result Proved the static vacuum extension conjecture is not true in general.
Survey of Baum-Connes conjecture history and methods.
problem Baum-Connes conjecture in mathematics.
method History and methods of the conjecture.
result Current status of the conjecture.
Calabi Conjecturemath.DG
This memoire consists of two main results. In the first one we describe Ricci flow theory and we give an educative way for proving Elliptization Conjecture and then we prove Poincare conjecture which is the second proof of Perelman for Poincare conjecture. In the second one which is the main propose of our memoire, we …