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.
The paper examines conditions for contact surgeries on rational homology 3-spheres.
We study invariant contact p-spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact p-spheres can only exist on (4n-1)-dimensional manifolds and we construct examples of contact p-spheres on such manifolds. We also consider relations between taut…
A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of …
Study finds all Brieskorn spheres with at most two fillable contact structures.
Study shows convex contact spheres resemble contact ellipsoids.
We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries along all transverse knots not isotopic to the transverse unknot with self-lin…
We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.
New contact structures on spheres and tori with weakly compatible metrics.
The paper defines a new structure on tangent sphere bundles and characterizes their properties.
Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.
The study finds many tight contact structures on hyperbolic 3-spheres.
The paper defines and studies contact surgery numbers for contact 3-manifolds.
In this note we show that a closed oriented contact manifold is obtained from the standard contact sphere of the same dimension by contact surgeries on isotropic and coisotropic spheres. In addition, we observe that all closed oriented contact manifolds admit symplectic caps.
Analytic torsions on contact spheres are calculated using Rumin complex.
Study shows magnetic trajectories in Berger spheres are homogeneous.
In this paper we study embeddings of contact manifolds using braidings of one manifold about another. In particular we show how to embed many contact 3-manifolds into the standard contact 5-sphere. We also show how to obstruct braidings of one manifold about another using contact geometry.
Real algebraic structures help classify overtwisted contact 3-spheres.
Contact group retracts to unitary subgroup.
Study contact structures on specific manifolds, proving infinite non-isotopic structures and tight/overtwisted classifications.
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness results on positively curv…
We study compatible contact structures of fibered Seifert multilinks in homology 3-spheres and especially give a necessary and sufficient condition for the contact structure to be tight in the case where the Seifert fibration is positively twisted. As a corollary we determine the strongly quasipositivity of fibered Sei…
The study constructs K-contact manifolds with minimal closed Reeb orbits and provides conditions for their homeomorphism to spheres.
Characterizes invariant contact metric structures on tangent sphere bundles of compact symmetric spaces.
It is known that for every smooth great circle fibration of the 3-sphere, the distribution of tangent 2-planes orthogonal to the fibres is a contact structure, in fact a tight one, but we show here that, beginning with the 5-sphere, there exist smooth great circle fibrations of all odd-dimensional spheres for which the…
Study on contact type hypersurfaces in 4-space, proving no Brieskorn spheres can embed.
New contact structures found on Brieskorn spheres.
In this short note, we exhibit an infinite family of hyperbolic rational homology --spheres which do not admit any fillable contact structures. We also note that most of these manifolds do admit tight contact structures.
Study extends contact cosmetic surgeries to non-trivial Legendrian knots in L-spaces.
A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry an…
Article generalizes open book construction for 5D contact pairs.
We prove various results on contact structures obtained by contact surgery on a single Legendrian knot in the standard contact three--sphere. Our main tool are the contact Ozsvath--Szabo invariants.
Contact surgeries yield algebraically overtwisted manifolds.
Defines contact surgery distance and shows it's bounded by topological surgery distance by 5.
The study constructs and shows isotopy of high-dimensional Legendrian spheres.
New method shows some 3D shapes can't be filled in certain ways.
Given a transverse link in the standard contact 3-sphere, we study the contact manifold that arises as a branched double cover of the sphere. We give a contact surgery description of such manifolds, which allows to determine the Heegaard Floer contact invariants for some of them. By example of the knots of Birman--Mena…
We prove the existence of exotic but homotopically trivial contact structures on spheres of dimension 8k-1. Together with previous results of Eliashberg and the second author this establishes the existence of such structures on all odd-dimensional spheres (of dimension at least 3).
We give new tightness criteria for positive surgeries along knots in the 3-sphere, generalising results of Lisca and Stipsicz, and Sahamie. The main tools will be Honda, Kazez and Matic's, Ozsvath and Szabo's Floer-theoretic contact invariants. We compute the Ozsvath and Szabo's invariant of positive contact surgeries …
Contractibility of tight contact structures on proven.
We compute the Ozsváth--Szabó contact invariants for all tight contact structures on the manifolds -Σ(2,3,6n-1).
Study contact structures on four-punctured spheres, finding infinitely many overtwisted monodromies.
In this paper we prove that the closed -ball admits non-Kähler complex structures with strictly pseudoconcave boundary. Moreover, the induced contact structure on the boundary -sphere is overtwisted.
Computes knot filtered ECH for torus knots on tight 3-sphere.
Quantizes contact structures using dynamical methods.
We characterize L-spaces which are Seifert fibered over the 2-sphere in terms of taut foliations, transverse foliations and transverse contact structures. We give a sufficient condition for certain contact Seifert fibered 3-manifolds with e_0=-1 to have nonzero contact Ozsvath--Szabo invariants. This yields an algorith…
In this paper we study the groups of contactomorphisms of a closed contact manifold from a topological viewpoint. First we construct examples of contact forms on spheres whose Reeb flow has a dense orbit. Then we show that the unitary group U(n+1) is homotopically essential in the group of contactomorphisms of the stan…
We show that there exists a transverse link in the standard contact structures on the 3-sphere such that all contact 3-manifolds are contact branched covers over this transverse link.
Monopole invariant studies contact structures on 3-manifolds.