Classifies involutions on spherical 3-manifolds.
problem Classifying involutions on spherical 3-manifolds.
method Geometric approach to conjugacy classification.
result Insights into topological properties of involutions.
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48 results for “Spherical Topology”
Harmonic analysis on Platonic spherical manifolds reveals selection rules.
problem Understanding harmonic analysis on different Platonic spherical three-manifolds.
method Starting from homotopies, converting to deck operations, constructing fundamental domains, and selecting subbases.
result Selection rules derived from spherical orbifolds have applications in cosmic topology.
Study on spherical CR manifolds with non-trivial Chern classes.
problem Understanding Chern classes in spherical CR manifolds.
method Construction and proof of constraints on Chern classes.
result Topological obstruction to spherical CR structures on contact manifolds.
This paper studies the topology of the constant energy surfaces of the double spherical pendulum.
The paper classifies and studies symplectic and contact properties of circular spherical divisors.
problem Investigating symplectic and contact topology of circular spherical divisors.
method Classification and analysis of concave circular spherical divisors, including embedding, Stein fillability, and rational homology type determination.
result All concave circular spherical divisors up to toric equivalence are realized as symplectic log Calabi-Yau pairs with minimal complements.
The paper classifies Poincaré complexes as topological manifolds.
problem Classifying Poincaré complexes as topological manifolds.
method Using spherical fibrations and CW-complexes, the paper proves stability and homotopy equivalence.
result A sufficient condition for Poincaré complexes to be homotopy types of topological manifolds.
Dunkl connections on complex plane don't preserve metrics.
problem Preserving metrics with Dunkl connections on \(\mathbb{C}^2\).
method Analysis of the topology of spherical tori with conical points.
result General Dunkl connections on \(\mathbb{C}^2\) do not preserve non-zero Hermitian forms.
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a survey of some of the main results and a guide to the literature.
In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of , this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3…
Study on metrics with positive scalar curvature on spherical space forms.
problem Determining metrics with positive scalar curvature on spherical space forms.
method Analysis of moduli spaces of metrics with positive scalar curvature on topological spherical space forms.
result Determination of the number of path components of moduli spaces for dimensions at least 5 and non-simply connected forms.
Random spherical harmonics on have a single nodal component with expected genus proportional to .
problem Understanding the topology of nodal sets of random spherical harmonics.
method Analyzing the real and imaginary parts of equivariant spherical harmonics on .
result The expected genus of nodal sets is proportional to for fixed .
New spherical T-duality for higher degree forms in fiber bundles.
problem Extending T-duality to higher degree forms in fiber bundles.
method Generalizing T-duality to -bundles with closed odd forms of arbitrary degree.
result Existence and isomorphic twisted cohomology of -dual spaces.
Proof of conjecture for spherical Artin groups.
problem Proving the conjecture for Artin groups of spherical type.
method Combining combinatorial topology with methods from the original proof of the spherical case.
result Proof of the conjecture for Artin groups of spherical type.
Spherical Knot Mosaicsmath.GT
Paper introduces spherical knot mosaics for knot and link invariants.
problem Representing knots on a sphere with tiles.
method Tiling a 2-sphere with 11 knot mosaic tiles to define new invariants.
result New knot invariants derived from spherical mosaic tiling.
New spherical Milnor spaces for diffeological groups with geometric and topological properties.
problem Understanding higher topological structures in diffeological spaces.
method Spherical Milnor construction based on quadratic normalization.
result Provides a natural setting for studying principal bundles with -twists and higher cohomology.
This paper introduces quantum invariants for 3-alterfolds and proves their consistency with topological moves.
problem Quantum invariants for 3-alterfolds and their consistency with topological moves.
method Introduction of 3-alterfolds with embedded separating surfaces and spherical fusion categories.
result Quantum invariants of 3-alterfolds are consistent with topological moves and generalize invariants of 3-manifolds containing framed links.
Introduces thin-thick decomposition for real isolated singularities.
problem Classifying real isolated singularities.
method Introduces thin-thick decomposition as a blow-spherical invariant.
result Generalizes thin-thick decomposition for complex surface singularities to real isolated singularities.
The paper explores the topology of compact Einstein manifolds, proving conditions for them to be homological spheres or spherical space forms.
problem Understanding the relationship between the curvature of compact Einstein manifolds and their topological properties.
method Proves conditions for compact Einstein manifolds to be homological spheres or spherical space forms based on sectional curvatures.
result Compact Einstein manifolds with positive Einstein constant are homological spheres under certain curvature conditions.
Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum Enveloping Algebra of sl(2). This invariant can be considered as a spherical version…
The paper studies the topology of spherical tori with one conical point.
problem Determining the topology of surfaces with constant curvature and conical points.
method Analyzing the moduli space of genus one surfaces with a conical point of specific angles.
result The moduli space topology depends on the integer for , and it has a complex structure for .
String-net models explore non-spherical fusion categories, revealing new spin structures and representations.
problem Investigating string-net models in non-spherical fusion categories.
method String-net models associate vector spaces to surfaces in terms of graphs decorated by objects and morphisms of a pivotal fusion category.
result String-net spaces count r-spin structures and carry representations of the mapping class group.
Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.
problem Future stability of expanding FLRW solutions with spatial topology R^3.
method Nonlinear stability analysis of spherically symmetric perturbations.
result Decay rates of energy momentum tensor components compared to Minkowski space.
The study connects curvature operators' positivity to manifold topology.
problem Positivity of curvature operators and their geometric implications.
method Analysis of Garding cones and positivity properties of curvature operators.
result Shifted cone conditions on curvature operators constrain manifold topology.
The study finds the minimum mass for bi-axisymmetric black holes with spherical topology.
problem Finding the minimum mass for bi-axisymmetric black holes.
method Analyzing extreme Myers-Perry initial data for 5-dimensional spacetimes.
result Proves the mass-angular momentum inequality for bi-axisymmetric black holes.
Spherical Plateau problem studies minimal surfaces in quotients of spheres.
problem Minimal surfaces in quotients of spheres.
method Metric currents, barycenter map method.
result Intrinsic uniqueness of solutions for negatively curved manifolds.
Constructs a new invariant for 4-manifolds and 3+1 TQFTs.
problem Developing a new invariant for 4-manifolds and 3+1 TQFTs.
method Using a G-crossed braided spherical fusion category to construct a state-sum type invariant.
result Introduces a new invariant for 4-manifolds and 3+1 TQFTs.
Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systemshep-th
Study connects Chern-Simons theory and topological strings on spherical Seifert manifolds.
problem Relating Chern-Simons theory and topological strings on spherical Seifert manifolds.
method Proposes a dual description using topological strings and integrable systems.
result Identifies the expansion of the LMO invariant with a Gromov-Witten/Donaldson-Thomas partition function.
A spherical topological manifold of dimension n-1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of…
A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >= 3 a complete locally-convex (topological) immersion of a connected (n-1)-manifold into the n-sphere is a surjection onto the boundary of a c…
Isothermic nets created from special maps for smooth surfaces.
problem Creating discrete curvature lines on surfaces.
method Special discrete holomorphic maps and lifted-folding.
result Isothermic nets with spherical parameter lines constructed efficiently.
Study shows negatively curved manifolds' spherical volume equals minimal surface area.
problem Understanding the spherical volume of negatively curved manifolds.
method Combining metric currents theory and limits of hyperbolic groups' representations.
result Spherical volume of negatively curved manifolds equals minimal surface area.
We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity assumption and for torsion-free fundamental groups they are still diff…
Study proves existence of closed geodesics on spheres and projective spaces.
problem Proving the existence of closed geodesics on Finsler metrics.
method Topological methods and Lusternik-Schnirelmann-type approach, using spherical complexities.
result Existence of multiple closed geodesics and upper bounds on their lengths.
A solution to the problem of topological classification of real cubic fourfolds is presented. It is shown that the real locus of a real non-singular cubic fourfold is obtained from a projective 4-space either by adding several trivial one- and two-handles, or by adding a spherical connected component.
The study characterizes compact submanifolds with pinched Ricci curvature in Euclidean and spherical space forms.
problem Characterizing compact submanifolds with specific Ricci curvature bounds.
method Proving rigidity results for submanifolds with Ricci curvature bounded below by a function of mean curvature.
result Submanifolds are either isometric to the Einstein Clifford torus or have vanishing homology groups up to a certain degree.
This paper connects geometric diagrams to spherical T-duality.
problem Establishing equivalence between geometric and string-theory frameworks.
method Introducing -diagrams and proving their equivalence to spherical T-dual pairs.
result Concrete geometric realization of spherical T-duality.
The study connects taut contact circles to transversely holomorphic flows on spherical 3-manifolds.
problem Classifying taut contact circles on spherical 3-manifolds.
method Relating taut contact circles to transversely holomorphic flows, using complex analogues of classical invariants.
result Derivation of rigidity statements and a uniformisation theorem for orbifolds.
We give sufficient conditions for a noncompact Riemannian manifold, which has quadratic curvature decay, to have finite topological type with ends that are cones over spherical space forms.
Proves nonnegatively curved hypersurfaces on a sphere are convex disks.
problem Characterizing nonnegatively curved hypersurfaces with free boundary on a sphere.
method Analyzes hypersurfaces in Euclidean space with constant mean curvature.
result Compact hypersurfaces are embedded convex disks.
Study dihedral spherical surfaces and their foliations.
problem Characterize dihedral spherical surfaces and their foliations.
method Define and analyze dihedral surfaces and their foliations, introduce geometric decompositions and deformations.
result Determine the dimension of the moduli space for dihedral surfaces.
From the homotopy groups of two cubic spherical 3-manifolds we construct the isomorphic groups of deck transformations acting on the 3-sphere. These groups become the cyclic group of order eight and the quaternion group respectively. By reduction of representations from the orthogonal group to the identity representati…
The paper lifts spherical Morse functions to immersions and embeddings.
problem Lifting spherical Morse functions to other maps.
method New methods to lift to special generic maps with non-positive codimensions.
result Constructs most lifts to special generic maps.
The study proves that certain hypersurfaces in elliptic space forms are topologically rigid.
problem Characterizing the topological structure of hypersurfaces in elliptic space forms.
method Proving topological rigidity under curvature constraints and using the Gauss map.
result Hypersurfaces in elliptic space forms are diffeomorphic to spheres or their quotients.
Enhanced bounds on rho-invariants for 3-manifolds.
problem Establishing bounds on Cheeger-Gromov rho-invariants for 3-manifolds.
method Constructing chain null-homotopies with linear complexity.
result Linearly bounded complexity of constructed null-homotopies.
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to , but does not topologically split. The second space satisfies…
Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded belowmath.DG
Study confirms conjectures on Ricci limit spaces and their topological properties.
problem Understanding the topological structure of noncollapsed Ricci limit spaces.
method Analysis of tangent cones and application of manifold recognition theorems.
result Cross-sections of tangent cones at points in 4D spaces are homeomorphic to a fixed spherical space form.
The study proves manifolds with positive scalar curvature can be decomposed into spherical and toroidal pieces.
problem Proving manifolds with positive scalar curvature can be decomposed into simpler pieces.
method Using a topological approach, the researchers prove a decomposition theorem for manifolds with positive scalar curvature and subquadratic decay.
result The manifold carries a complete Riemannian metric of uniformly positive scalar curvature, answering a conjecture of Gromov.
Classifies 3-manifolds with uniformly positive scalar curvature.
problem Classifying 3-manifolds with uniformly positive scalar curvature.
method Analyzes properties of 3-manifolds with mean convex boundaries and uniformly positive scalar curvature.
result 3-manifolds with uniformly positive scalar curvature are homeomorphic to sums of spherical 3-manifolds and .