arXiv research

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…

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…

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…

Paper proves equivariant Fried conjecture for specific flows.

New method shows pseudo-Anosov flows on graph manifolds can be simplified.

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…

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the …

The study finds infinitely many periodic orbits that can be used to modify Anosov flows.

Find limiting sets for digital cones and suspensions.

Geodesic flow on orbifolds has a genus 1 Birkhoff section.

Study of Hermitian structures on toric suspensions of balanced manifolds.

New metrics found on non-Kähler Calabi-Yau manifolds.

Study simplifies homotopy groups of 6D manifolds.

Study Anosov representations of reducible suspensions of hyperbolic groups.

Study of flows on 7D manifolds with holomorphic properties.

Suspensions of manifolds by circle surgeries are key in free action constructions.

Let Q be a component of a stratum of abelian or quadratic differentials on an oriented surface of genus $g\geq 0$ with $m\geq 0$ punctures and $3g-3+m\geq 2$. We construct a subshift of finite type $(Ω,σ)$ and a Borel suspension of $(Ω,σ)$ which admits a finite-to-one semi-conjugacy into the Teichmueller flow $Φ^t$ on …

Study cohomotopy sets of simply connected 7-manifolds using suspension decompositions.

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.

Smoothly conjugate Anosov flows on 3D manifolds are actually smoothly conjugate.

The article shows how to create metrics with positive Ricci curvature on twisted suspensions.

Symbolic dynamics for flows in high dimensions, extending previous work.

Geometric models for algebraic suspensions using affine deformation spaces.

Maps on infinite-type surfaces linked to 3-manifold flows.

Study of flows on complex manifolds with holomorphic properties.

In this article we study the topological structure of the lifts to the universal of the stable and unstable foliations of $3$-dimensional Anosov flows. In particular we consider the case when these foliations do not have Hausdorff leaf space. We completely determine the structure of the set of non separated leaves from…

We first prove rigidity results for pseudo-Anosov flows in prototypes of toroidal 3-manifolds: we show that a pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically equivalent to a geodesic flow and we show that a pseudo-Anosov flow in a solv manifold is topologically equivalent to a susp…

Characterizes transverse surfaces for pseudo-Anosov flows in 3-manifolds.

Classifies Anosov flows on figure-eight knot surgeries.

Study of spectral flow in symmetric Toeplitz operator families.

The paper examines geometric invariants near a specific type of singular point.

New infinite family of 2-complexes intrinsically linked in 4D.

Study determines homotopy types of specific 6-manifolds.

Geometric quantization for specific symplectic structures proved.

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…

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…

A locally conformally Kaehler (l.c.K.) manifold is a complex manifold admitting a Kaehler covering $\tilde M$, with each deck transformation acting by Kaehler homotheties. A compact l.c.K. manifold is Vaisman if it admits a holomorphic flow acting by non-trivial homotheties on $\tilde M$. We prove a structure theorem f…

Machine learning predicts phase behavior in active matter suspensions.

Given a general pseudo-Anosov flow in a three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We compactify this orbit space with an ideal circle boundary. If there are no perfect fits between stable and unstable leaves and the flow is not topologically conjugate to …

Study homotopy types of 4-manifolds, finding decompositions and conditions for desuspension.

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 $L^m_{p,q}$ (respectively, $C^{m-p}_p$) the group of smooth embeddings $S^p\sqcup S^q\to S^m$ (respectively, $S^p\to S^m$) up to smooth isotopy. Denote by $LM^m_{p,q}$ the …

We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.

This paper uses Heegaard Floer theory to study pseudo-Anosov flows and their periodic points.

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 map connects 3-manifold quantizations.

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.