Paper shows certain generalized Whitney topologies are Baire.
problem Understanding the Baire property in generalized Whitney topologies.
method Analyzing intersections of open and dense sets.
result Generalized Whitney topologies are Baire.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Whitney $C^k$-topology”
Stiefel-Whitney classes of moment-angle manifolds are trivial.
problem Analyzing the topological properties of moment-angle manifolds.
method Proving triviality of Stiefel-Whitney classes for moment-angle manifolds, including partial quotients.
result Stiefel-Whitney classes of moment-angle manifolds are trivial.
We prove that the group D^r(R) of C^r diffeomorphisms of the real line, endowed with the compact-open and Whitney C^r topologies, is bihomeomorphic to the group H(R) of homeomorphisms of the real line endowed with the compact-open and Whitney topologies. This implies that the diffeomorphism group D^r(R) endowed with th…
Paper proves Whitney stratified spaces can be given a conically smooth structure.
problem Proving Whitney stratified spaces can be given a conically smooth structure.
method Introduced conically smooth structure by Ayala, Francis, and Tanaka. Proved conjecture that any Whitney stratified space admits a canonical conically smooth structure.
result Established a connection between Whitney stratified spaces and conically smooth spaces.
Geometric trick simplifies link homotopy and concordance.
problem Homotopy and concordance of links in homology spheres.
method Relative Whitney trick to remove double points.
result Links in homology spheres can be simplified to topologically slice links.
We prove that for any non-compact connected surface the group of compactly suported homeomorphisms of endowed with the Whitney topology is homeomorphic to or .
Many open problems and important theorems in low-dimensional topology have been formulated as statements about certain 2--complexes called gropes. This paper describes a precise correspondence between embedded gropes in 4--manifolds and the failure of the Whitney move in terms of iterated `towers' of Whitney disks. The…
The paper shows how to approximate continuous maps to smooth CW complexes.
problem Approximating continuous maps to smooth CW complexes.
method Whitney Approximation Theorem for continuous maps to smooth CW complexes.
result Topological CW complexes are homotopy equivalent to smooth CW complexes.
Stable convex integrands are open and dense in smooth convex integrands.
problem Characterizing stability of convex integrands.
method Whitney topology analysis.
result Set of stable convex integrands is open and dense.
Proves generic condition is satisfied for all metrics in a residual set.
problem Singularity theorems in general relativity.
method Proves generic condition in Whitney -topology for all metrics in a residual set.
result Generic condition is satisfied for all metrics in a residual set.
We show how to measure the failure of the Whitney trick in dimension 4 by constructing higher- order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previous…
Computes the group of link homotopy classes of 2-spheres in 4-space.
problem Computing the group of link homotopy classes of link maps of 2-spheres into 4-space.
method Geometric constructions and algebraic duals of immersed Whitney disks.
result The group is free abelian, generated by specific constructions and detected by invariants.
Let X be a locally compact Polish space and G a non-discrete Polish ANR group. By C(X,G), we denote the topological group of all continuous maps f:X \to G endowed with the Whitney (graph) topology and by C_c(X,G) the subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete…
For a non-compact n-manifold M let H(M) denote the group of homeomorphisms of M endowed with the Whitney topology and H_c(M) the subgroup of H(M) consisting of homeomorphisms with compact support. It is shown that the group H_c(M) is locally contractible and the identity component H_0(M) of H(M) is an open normal subgr…
The paper defines a stratification for Lie groupoids in a tame topology context.
problem Presenting a tame topology counterpart to canonical stratification of Lie groupoids.
method Using Shiota's isotopy lemma and approximation theorem, the paper defines a canonical Whitney stratification of definable Lie groupoids into invariant strata.
result A canonical Whitney stratification of the Lie groupoid into definable strata invariant under the groupoid action.
A new theorem eliminates higher-multiplicity intersections in manifold topology.
problem Eliminating intersections in manifold topology, especially in higher dimensions.
method Proved and applied the -fold Whitney trick for proper maps from disjoint unions of disks to -dimensional balls.
result A continuous map can be modified to avoid intersections in higher dimensions.
Study shows knots in homology spheres can be topologically equivalent to those in .
problem Distinguishing knots in homology spheres from those in .
method Whitney tower filtration of concordance and solvable filtration.
result Every knot (or link) in a homology sphere is equivalent to a knot (or link) in modulo any term in the Whitney tower filtration.
Study Hamiltonian formalisms of degenerate gravity Lagrangians.
problem Hamiltonian analysis of degenerate gravity Lagrangians.
method Employed Dirac-Bergmann constraint algorithm and Gotay-Nester-Hinds algorithm.
result Total Hamiltonian functions and Hamilton's equations derived.
Coupled embeddabilitymath.GT
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
problem Understanding when maps on products of spaces can be embedded.
method Uses known results for nonsingular biskew and bilinear maps, studies genericity properties, extends Whitney embedding theorems, and relates to -coindex of embedding spaces.
result Generates strong obstructions to coupled embeddability in terms of combinatorics of triangulations.
New method maps simplicial complexes into higher dimensions without multiple intersections.
problem Eliminating multiple intersections in maps of simplicial complexes.
method Higher-multiplicity Whitney trick and Deleted Product Criterion.
result Necessary and sufficient conditions for maps without r-Tverberg points.
Suppose M is a non-compact connected n-manifold without boundary, DD(M) is the group of C^\infty-diffeomorphisms of M endowed with the Whitney C^\infty-topology and DD_0(M) is the identity connected component of DD(M), which is an open subgroup in the group DD_c(M) \subset DD(M) of compactly supported diffeomorphisms o…
Classifies 5-manifolds with free fundamental group and simple boundary links.
problem Classifying 5-manifolds with specific properties.
method Using algebraic topology, including homotopy groups, cohomology, and Stiefel-Whitney classes.
result Complete algebraic picture of 5-manifolds with free fundamental group and trivial second homology.
We construct many examples of non-slice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional topological knot concordance group. The bottom part of the filtration exhibits all…
Study on unknotted gropes and Whitney towers in 4-sphere.
problem Understanding unknottedness of gropes and Whitney towers.
method Introduced unknottedness of gropes and Whitney towers, proved preservation under modifications, constructed handlebody structures.
result Bi-filtrations of knots do not stabilize, approximating double sliceness.
A criterion for Whitney disks connects intersections in 3-manifold homology.
problem Existence of Whitney disks in Heegaard Floer homology.
method Use Nielsen theory to establish a criterion.
result Simple criterion for the existence of Whitney disks.
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is -regular. Here…
Notes on Whitney towers in 4-manifolds, focusing on local surface manipulations and invariants.
problem Classifying and understanding Whitney towers in 4-manifolds.
method Local manipulations of surfaces, definitions of Whitney towers and trees, geometric Jacobi identities, classification of twisted Whitney towers.
result Classification of order n twisted Whitney towers in the 4-ball and related invariants.
Stably exotic 4-manifoldsmath.GT
New stable exotic 4-manifolds found with specific topological properties.
problem Identifying conditions for the existence of stable exotic 4-manifolds.
method Investigated fundamental group, Stiefel-Whitney classes, and H_5(π;Z) to determine stable exotic pairs.
result Produced new stable exotica and settings where they do not arise.
This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new qua…
Study on curves around a Whitney umbrella focusing on geodesic and normal curvatures.
problem Analyzing geometric properties of curves around a specific surface.
method Examined geodesic and normal curvatures, ruled surfaces, and normal developable surfaces.
result Obtained functions representing geometry on a Whitney umbrella.
Classifies links in 3-sphere using Whitney towers in rational homology 4-ball.
problem Classifying links in 3-sphere using geometric methods.
method Complete classifications of links using Whitney towers in rational homology 4-ball.
result Geometric characterization of Milnor invariants and higher order Arf invariants.
Paper examines stability of non-proper smooth functions.
problem Stability of non-proper smooth functions.
method Analyzes properties of Morse and Nash functions to establish stability conditions.
result Shows existence of stable but not infinitesimally stable functions.
In his study of the group of homology cylinders, J. Levine made the conjecture that a certain homomorphism eta': T -> D' is an isomorphism. Here T is an abelian group on labeled oriented trees, and D' is the kernel of a bracketing map on a quasi-Lie algebra. Both T and D' have strong connections to a variety of topolog…
We study the topology of the inertia space of a smooth -manifold where is a compact Lie group. We construct an explicit Whitney stratification of the inertia space, demonstrating that the inertia space is a triangulable differentiable stratified space. In addition, we demonstrate a de Rham theorem for differ…
New proof using Bochner technique for compact surfaces.
problem Proving a classical result about compact surfaces.
method Application of Bochner formula and Whitney embedding theorem.
result Compact orientable surfaces with no tangent vector field zeroes are diffeomorphic to a torus.
Let M be a riemannian manifold. The existence of a spin structure on M, enables to study the topology of M. The obstruction to the existence of the spin structure is given by the second Stiefel-Whitney class. This class is the classifying cocycle of a gerbe. One may expect that the study of this gerbe may have topologi…
Study connects knot invariants to Whitney tower data.
problem Understanding abelian invariants of knots.
method Relates invariants to intersection data of Whitney towers.
result New algorithm for computing knot invariants.
For a topological space we study continuous maps such that images of every pairwise distinct points are affinely (linearly) independent. Such maps are called affinely (linearly) -regular embeddings. We investigate the cohomology obstructions to existence of regular embeddings and give …
Constructs Riemannian manifolds to approximate metric spaces.
problem Approximating a metric space with a Riemannian manifold.
method Constructs a Riemannian manifold to approximate a metric space .
result Characterizes metric spaces that can be approximated by Riemannian manifolds.
Lagrangian spheres develop singularities under flow, matching Whitney spheres.
problem Understanding singularities in Lagrangian mean curvature flow.
method Analyzing equivariant Lagrangian spheres with Ricci curvature conditions.
result Whitney spheres develop type-II singularities rescaling to a grim reaper and flat subspace.
Link concordance and Whitney towers linked to Milnor invariants.
problem Link concordance and Whitney towers classification.
method Clasper surgeries, Whitney towers, and Milnor invariants.
result Link concordance and Whitney towers classified in terms of Milnor invariants.
This paper describes grope and Whitney tower filtrations on the set of concordance classes of classical links in terms of class and order respectively. Using the tree-valued intersection theory of Whitney towers, the associated graded quotients are shown to be finitely generated abelian groups under a (surprisingly) we…
We introduce a notion of symmetric Whitney tower cobordism between bordered 3-manifolds, aiming at the study of homology cobordism and link concordance. It is motivated by the symmetric Whitney tower approach to slicing knots and links initiated by Cochran, Orr, and Teichner. We give amenable Cheeger-Gromov rho-invaria…
Study shows Whitney sphere collapses to a point in finite time.
problem Understanding the evolution of Whitney sphere under mean curvature flow.
method Investigated equivariant Lagrangian spheres in \(\mathbb{C}^n\) using mean curvature flow.
result Equivariant Lagrangian spheres collapse to a point in finite time and converge to a plane with multiplicity two.
The Dold-Whitney theorem helps classify bundles and gives a mod 4 slice obstruction.
problem Classifying -bundles and determining sliceability of links.
method Using the Dold-Whitney theorem to classify bundles and relate to the Sato-Levine invariant.
result The Dold-Whitney theorem's mod 4 obstruction coincides with the Sato-Levine invariant.
New method computes link invariants using special Whitney towers.
problem Computing link invariants for 2-component links.
method Cochran towers, special types of twisted Whitney towers.
result Simultaneous computation of invariants for all from a single tower of order .
Extends functions on symmetric spaces to analytic functions.
problem Extending functions on symmetric spaces to analytic functions.
method Harmonic analysis on symmetric spaces and representation theory of groups.
result Proves Whitney type extension theorems for symmetric spaces.
The Whitney sphere has a unique energy gap for a specific equation.
problem Energy gap phenomenon for the Whitney sphere.
method Solving the equation on Lagrangian surfaces.
result Proves a gap theorem for the Whitney sphere.