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 study finds many tight contact structures on hyperbolic 3-spheres.
For any n\ge 2, we give infinitely many unsplittable links of n components in the 3-sphere which admit non-trivial surgery yielding the 3-sphere again and whose components are mutually distinct hyperbolic knots. Berge and Kawauchi gave 2-component hyperbolic links with those two properties. We can also give infinitely …
In this paper, we characterize non-hyperbolic 3-component links in the 3-sphere whose exteriors contain essential 3-punctured spheres with non-integral boundary slopes. We also show the existence of embeddings of some multibranched surfaces in the 3-sphere which satisfy some homological conditions to be embedded in the…
Hyperbolic links in handlebodies can be composed, unlike in 3-sphere.
Hyperbolic 3-manifolds can be approximated by removing Cantor sets from the 3-sphere.
6 out of 29 dodecahedral 3-spheres are L-spaces, solving a Seiberg-Witten question.
For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic 3-manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed 3-manifold containing an incompressible torus. The slope corresponding to a toroidal surgery, called a toroidal s…
We obtain explicit, isometry-invariant integral formulas for twisting, writhing and helicity, and prove the theorem LINK = TWIST + WRITHE on the 3-sphere and in hyperbolic 3-space. We then use these results to derive upper bounds for the helicity of vector fields and lower bounds for the first eigenvalue of the curl op…
We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere.
We prove that for every $\Q$-homological Finsler 3-sphere with a bumpy and irreversible metric , either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.
The branched virtual fibering theorem by Sakuma states that every closed orientable -manifold with a Heegaard surface of genus has a branched double cover which is a genus surface bundle over the circle. It is proved by Brooks that such a surface bundle can be chosen to be hyperbolic. We prove that the minim…
We introduce here explicit integral formulas for linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space. These formulas, like their prototypes in Euclidean 3-space, are geometric rather than just topological, in the sense that their integrands are invariant under orientation-preserving isome…
We construct hyperbolic integer homology 3-spheres where the injectivity radius is arbitrarily large for nearly all points of the manifold. As a consequence, there exists a sequence of closed hyperbolic 3-manifolds which Benjamini-Schramm converge to H^3 whose normalized Ray-Singer analytic torsions do not converge to …
The study of symmetries in manifolds derived from colored polytopes.
It is shown that a hyperbolic knot in the 3-sphere admits at most nine integral surgeries yielding 3-manifolds which are reducible or whose fundamental groups are not infinite word-hyperbolic.
For a hyperbolic knot in the 3-sphere, the distance between toroidal surgeries is at most 5, except the figure eight knot. In this paper, we determine all hyperbolic knots that admit two toroidal surgeries with distance 5.
The study limits the number of ribbon concordant fibered knots.
Identifies a mod- triple cup product for rational homology 3-spheres with specific first homology.
Paper finds new 3D shapes that can be inside a 4D space.
We consider the space of all smooth knots in the 3-sphere isotopic to a given knot, with the aim of finding a small subspace onto which this large space deformation retracts. For torus knots and many hyperbolic knots we show the subspace can be taken to be the orbit of a single maximally symmetric placement of the knot…
Constructs chiral rational homology spheres with hyperbolic groups.
The main result of this paper is that any -dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable twisted coefficients as well. The following two consequences motivated this work. First, there are hyperbolic equivarian…
In 1978, W. Thurston revolutionized low diemsional topology with his work on hyperbolic 3-manifolds. In this paper, we discuss what is currently known about knots in the 3-sphere with hyperbolic complements. Then focus is on geometric invariants coming out of the hyperbolic structures. This is one of a collection of ar…
Researchers create links in 3-sphere satisfying volume conjecture.
We exhibit an algorithm to determine the bridge number of a hyperbolic knot in the 3-sphere. The proof uses adaptations of almost normal surface theory for compact surfaces with boundary in ideally triangulated knot exteriors.
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 of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
The paper proves unique factorization of knotted handlebodies and examines handlebody-knot symmetry.
Infinitely many hyperbolic links in lens space have isotopic lifts in 3-sphere.
We show that all exceptional surgeries on hyperbolic alternating knots in the 3-sphere are integral surgeries.
This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In particular, it adds further evidence in favor of this conjecture by studying these t…
Constructs knots from 3-manifolds with specified geometric limits.
We analyze the orbifolds that can be obtained as quotients of hyperbolic 3-manifolds admitting a Heegaard splitting of genus two by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the hyperbolic 2-fold branched coverings of 3-bridge links. If the 3-bridge link is a knot, w…
A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c and twist K n times along c to obtain a twist family { K_n }. We give a sufficient…
Preserves hyperbolicity in link complements with two moves.
In this paper, we give a complete classification of exceptional Dehn surgeries on a component of a hyperbolic two-bridge link in the 3-sphere.
We show that there exist hyperbolic knots in the 3-sphere such that the set of points of large injectivity radius in the complement take up the bulk of the volume. More precisely, given a finite volume hyperbolic manifold, for any bound R>0 on injectivity radius, consider the set of points with injectivity radius at le…
The paper finds lower bounds on hyperbolic 3-manifold volumes.
A 4-manifold is constructed with some curious metric properties; or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious. Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on their complements play a role in this story.
In this first of two papers, we develop a steady-state version of classical electrodynamics on the 3-sphere and in hyperbolic 3-space, including an explicit formula for the vector-valued Green's operator, an explicit formula of Biot-Savart type for the magnetic field, and a corresponding Ampere's Law contained in Maxwe…
We prove that there are compact submanifolds of the 3-sphere whose interiors are not homeomorphic to any geometric limit of hyperbolic knot complements.
The paper determines the structure of Kakimizu complexes for genus one hyperbolic knots.
The paper constructs 3-manifolds with co-orientable taut foliations but no foliations with vanishing Euler class.
Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S^3? It is conjectured that if r-surgery on a hyperbolic knot in S^3 yields a Seifert fiber space, then r is an integer. We show that for each integer n, there exists a tunnel number one, hyperbolic knot K_n in S^3 such tha…
It is experimentally known that achiral hyperbolic 3-manifolds are quite sporadic at least among those with small volume, while we can find plenty of them as amphicheiral knot complements in the 3-sphere. In this paper, we show that there exist infinitely many achiral 1-cusped hyperbolic 3-manifolds not homeomorphic to…
Characterizes hyperbolic links with stable maps to the plane.
Random hyperbolic 3-manifolds can be obtained via Dehn surgery.
A knot in the 3-sphere is called an L--space knot if it admits a nontrivial Dehn surgery yielding an L--space. Like torus knots and Berge knots, many L--space knots admit also a Seifert fibered surgery. We give a concrete example of a hyperbolic, L-space knot which has no exceptional surgeries, in particular, no Seifer…