We provide a written proof of a result due to H. Minakawa, which states that all suspension Anosov flows generated by hyperbolic matrices with positive trace are pairwise almost equivalent. The proof relies on constructing, for any given suspension flow, a genus-one Birkhoff section whose first-return map has fewer fix…
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48 results for “suspension graphs”
The paper classifies when certain graph braid groups are 3-manifold groups.
problem Identifying when graph braid groups are 3-manifold groups.
method Analyzing the graph braid groups for specific graphs .
result The paper shows that is a 3-manifold group, but is not quasi-isometric to a 3-manifold group for .
New method shows pseudo-Anosov flows on graph manifolds can be simplified.
problem Understanding pseudo-Anosov flows on graph manifolds.
method Constructing a partial Birkhoff section with genus one components that misses finitely many closed orbits.
result Every pseudo-Anosov flow on a graph manifold is almost equivalent to a totally periodic flow or a suspension Anosov flow.
New infinite family of 2-complexes intrinsically linked in 4D.
problem Intrinsic linking of 2-complexes in 4D.
method Examining suspensions of graphs containing K6 as a minor.
result Embeddings of suspensions contain intrinsically linked cycles.
Machine learning predicts phase behavior in active matter suspensions.
problem Predicting phase behavior in active matter systems using machine learning.
method Used deep learning techniques, including fully connected networks and graph neural networks, to predict motility-induced phase separation (MIPS) in ABP suspensions.
result Strong agreement between machine learning predictions and MIPS binodal from simulations, suggesting machine learning as an effective method for phase behavior determination.
The paper studies pseudo-isotopies of spherical 3-manifolds and computes ranks of certain groups.
problem Computing ranks of abelian groups related to spherical 3-manifolds.
method Surgery on theta-graphs embedded in spherical 3-manifolds, study of pseudo-isotopy behavior under suspension.
result Lower bounds of ranks of abelian groups are computed.
Find limiting sets for digital cones and suspensions.
problem Digital topology cone and suspension constructions.
method Identify (m, n)-limiting sets, especially (0, 0)-freezing sets.
result Discover (0, 0)-limiting sets for digital cones and suspensions.
Study of Hermitian structures on toric suspensions of balanced manifolds.
problem Exploring Hermitian structures on specific types of manifolds.
method Analysis of toric suspensions of Calabi-Yau and hyperkähler manifolds under holomorphic automorphisms.
result Suspensions of hyperkähler manifolds do not admit certain Hermitian metrics.
Study simplifies homotopy groups of 6D manifolds.
problem Homotopy groups of 6D manifolds.
method Double suspension homotopy decomposition.
result Easily determines - and -groups.
Study Anosov representations of reducible suspensions of hyperbolic groups.
problem Characterize dynamical properties of reducible suspensions of Anosov representations.
method Analyzing linear representations of non-elementary hyperbolic groups, focusing on weak unipotent actions on subspaces.
result Characterize when reducible suspensions are discrete and faithful, quasi-isometrically embedded, and Anosov.
Suspensions of manifolds by circle surgeries are key in free action constructions.
problem Understanding free -actions on smooth manifolds of dimension at least 3.
method Circle surgeries on yield suspensions and .
result Suspension operations are fundamental in constructing and classifying manifolds with free -actions.
Study cohomotopy sets of simply connected 7-manifolds using suspension decompositions.
problem Understanding cohomotopy sets of simply connected 7-manifolds.
method Establish homotopy decompositions of the reduced suspension space into simpler spaces localized at primes.
result Established homotopy decompositions leading to insights into cohomotopy sets.
This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970's but never published. It presents the initial solutions of the fabled Double Suspension Conjecture. (The other two articles are: 'Approximating certain cell-like maps by homeomorphisms' and 'T…
In the paper of Montgomery, D. and Yang, C.T. [5], they discuss the de-suspension of smooth free actions of S1 on (2n+1)-dimensional homotopy spheres. In this paper we discuss the de-suspension of smooth free actions of S3 on (4n + 3)-dimensional homotopy spheres.
The article shows how to create metrics with positive Ricci curvature on twisted suspensions.
problem Creating metrics with positive Ricci curvature on complex manifolds.
method Using twisted suspensions and Riemannian metrics.
result Maximal symmetry rank of positive Ricci curvature manifolds is (n-2) in all dimensions n≥4.
Geometric models for algebraic suspensions using affine deformation spaces.
problem Analyzing which motivic homotopy types have smooth scheme representatives.
method Affine deformation spaces of embeddings provide models for -suspensions of schemes.
result Yields many examples of -connected and strictly quasi-affine schemes.
We introduce a representation via (n+1)-colored graphs of compact n-manifolds with (possibly empty) boundary, which appears to be very convenient for computer aided study and tabulation. Our construction is ageneralization to arbitrary dimension of the one recently given by Cristofori and Mulazzani in dimension three, …
The study finds infinitely many periodic orbits that can be used to modify Anosov flows.
problem Can surgeries on periodic orbits of Anosov flows produce equivalent flows?
method Analyzing suspension Anosov flows, the study identifies pairs of periodic orbits that can be used to modify the flow.
result For some suspension Anosov flows, there exist infinitely many pairs of periodic orbits that can be used to modify the flow.
Volume preserving codimension one Anosov flows in dimensions greater than three are suspensionsmath.DS
We show that every volume preserving codimension one Anosov flow on a closed Riemannian manifold of dimension greater than three admits a global cross section and is therefore topologically conjugate to a suspension of a linear toral automorphism. This proves a conjecture of Verjovsky from the 1970's in the volume pres…
Boundedness of geometric invariants near a singularity which is a suspension of a singular curvemath.DG
The paper examines geometric invariants near a specific type of singular point.
problem The behavior of geometric invariants near a singular point of a surface or curve.
method Analysis of geometric invariants for surfaces and curves that are suspensions of singular curves.
result Evaluation of the orders of Gaussian and mean curvatures for the studied surfaces and curves.
Study determines homotopy types of specific 6-manifolds.
problem Identify homotopy types of triple suspended 6-manifolds.
method Assumes trivial action of certain cohomology operation and uses triple suspension.
result Determines homotopy types of triple suspended 6-manifolds.
Geometric quantization for specific symplectic structures proved.
problem Quantization of specific symplectic structures.
method Geometric quantization for constant rank presymplectic structures with Riemannian null foliation.
result Quantization-commutes-with-reduction theorem proved in this context.
Let M be one of the projective spaces CP^n, HP^n for n>1 or the Cayley projective plane OP^2, and let LM denote the free loop space on M. Using Morse theory methods, we prove that the suspension spectrum of (LM)_+ is homotopy equivalent to the suspension spectrum of M_+ wedge a family of Thom spaces of explicit vector …
Almost forty years ago, C.T.C. Wall systematically analyzed the set of "thickenings" of a finite CW complex. Of the results he obtained, probably the most computationally important is the "suspension theorem," which is an exact sequence relating the n-dimensional thickenings of a finite complex to its (n+1)-dimensional…
Paper proves equivariant Fried conjecture for specific flows.
problem Equivariant Fried conjecture for suspension flows.
method Analyzes suspension flows of equivariant isometries.
result Proves conjecture for various groups and cases.
For a closed PL manifold M, we consider the configuration space F(M,k) of ordered k-tuples of distinct points in M. We show that a suitable iterated suspension of F(M,k) is a homotopy invariant of M. The number of suspensions we require depends on three parameters: the number of points k, the dimension of M and the con…
The topology of the Hausdorff leaf spaces (HLS) for a codim-1 foliation is the main topic of this paper. At the beginning, the connection between the Hausdorff leaf space and a warped foliations is examined. Next, the author describes the HLS for all basic constructions of foliations such as transversal and tangential …
For any toric automorphism with only real eigenvalues a Riemannian metric with an integrable geodesic flow on the suspension of this automorphism is constructed. A qualitative analysis of such a flow on a three-solvmanifold constructed by the authors in math.DG/9905078 is done. This flow is an example of the geodesic f…
Study homotopy types of 4-manifolds, finding decompositions and conditions for desuspension.
problem Determine homotopy types of double suspensions of 4-manifolds with 2-torsion.
method Use Postnikov square and analyze homology groups to find decompositions and conditions for desuspension.
result Homotopy decompositions of double suspensions as wedge sums of specific complexes.
We present a new short proof of the explicit formula for the group of links (and also link maps) in the 'quadruple point free' dimension. Denote by (respectively, ) the group of smooth embeddings (respectively, ) up to smooth isotopy. Denote by the …
We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.
The use of the trading halts is a practice common to all markets. However, the advantages and the disadvantages of the measurements are regularly discussed. The partisans think that the trading suspensions or the price limits make it possible to the investors to have time to react to the new information. The detractors…
3d Quantum Trace Mapmath.GT
3D quantum trace map connects 3-manifold quantizations.
problem Quantization of 3-manifold character varieties.
method Study of stated skein modules and face suspensions.
result Existence of 3D quantum trace map proved.
We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.
We construct a map from the suspension -spectrum of a smooth compact -manifold to the equivariant -theory spectrum , and we show that its fiber is, on fixed points, a wedge of stable -cobordism spectra. This map is constructed as a map of spectral Mackey functors, which is compatible …
Proves Farrell--Jones Conjecture for hyperbolic groups and their automorphisms.
problem Proving the Farrell--Jones Conjecture for automorphisms of hyperbolic groups.
method Analyzes JSJ decompositions and applies results to automorphisms of hyperbolic groups.
result Proves the fibred Farrell--Jones Conjecture for a class of relatively hyperbolic groups.
New results on algebraic knots with Brieskorn polynomials.
problem Understanding cobordisms of algebraic knots defined by Brieskorn polynomials.
method Analyzing Fox--Milnor type relations, decomposing algebraic cobordism classes, and studying cyclic suspensions.
result Spherical algebraic knots associated with Brieskorn polynomials have infinite order in the knot cobordism group.
Study rigidity of PSU(1,1) actions on circle via harmonic measures.
problem Rigidity properties of surface group actions on the circle.
method Foliated harmonic measures and curvature estimates.
result Curvature estimate and Gauss--Bonnet formula for connection.
New homology theory for graphs detects subdivisions and homology manifolds.
problem Defining a dissimilarity metric for graphs.
method Filtration on simplicial homology, using bi-colourings of vertices.
result The überhomology vanishes in lowest degree for subdivisions and coincides with fundamental class for homology manifolds.
In this note we give a simple, model-independent construction of Chern classes as natural transformations from differential complex K-theory to differential integral cohomology. We verify the expected behaviour of these Chern classes with respect to sums and suspension.
Study harmonic measures and rigidity in Seifert 3-manifolds using -connections.
problem Rigidity of foliations on Seifert 3-manifolds with maximal Euler number.
method Using -connections and harmonic measures, proving the Gauss--Bonnet formula and rigidity results.
result A harmonic measure on the suspension bundle of the action with maximal Euler number has rigidity, closely related to the Poisson kernel.
New metrics found on non-Kähler Calabi-Yau manifolds.
problem Finding Levi-Civita Ricci-flat metrics on non-Kähler Calabi-Yau manifolds.
method Constructing new metrics on specific types of non-Kähler Calabi-Yau manifolds.
result Examples of Levi-Civita Ricci-flat metrics on various non-Kähler Calabi-Yau manifolds.
Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwis…
We construct the coarse index class with support condition (as an element of coarse -homology) of an equivariant Dirac operator on a complete Riemannian manifold endowed with a proper, isometric action of a group. We further show a coarse relative index theorem and discuss the compatibility of the index with the sus…
Explains exceptional surgeries connecting maps and knot orbifolds.
problem Exceptional surgeries connecting maps and knot orbifolds.
method Explains connections between the cat-bat map and figure-eight knot via hyperbolic orbispheres.
result Shows how the suspension of the cat-bat map is related to figure-eight knot orbifolds.
We obtain a topological and equivariant classification of closed, connected three-dimensional Alexandrov spaces admitting a local isometric circle action. We show, in particular, that such spaces are homeomorphic to connected sums of some closed 3-manifold with a local circle action and finitely many copies of the susp…
New benchmarks improve model performance by accounting for isomorphism classes in multi-relational datasets.
problem Synthetic multi-relational datasets lack isomorphism class awareness, leading to overestimation of model performance.
method Proposed isomorphism-aware synthetic benchmarks and a prioritisation scheme to improve model performance and stability.
result Isomorphism classes can be utilised to improve model performance, stability during training, and reduce training time.
The study classifies discrete pseudomanifolds with up to 2d+7 vertices.
problem Understanding discrete pseudomanifolds with a small number of vertices.
method Proved existence of at least 2(d+1) vertices, classified up to 2d+6 vertices, established equivalence with edge graphs of flag normal pseudomanifolds.
result Every flag normal d-pseudomanifold with at most 2d+7 vertices is either a simplicial d-sphere or a flag triangulation of the (d-2)-fold suspension of RP^2.