arXiv research

We revisit the issue of the existence of infinitely many distinct prime knots with the same Alexander invariant. We present infinitely many distinct families, each family made up of infinitely many distinct knots. Within each family, the Alexander invariant is the same. Unlike other examples in the literature, ours are…

The paper proves the existence of maxfaces with multiple swallowtails and planar ends.

New infinite families of twisted torus knots found.

Infinite families of quantum modular invariants for 3-manifolds are discovered.

Infinite Klein bottles with 4-fold meridians found.

Paper proves knots satisfy a conjecture using Jones polynomial.

Infinite-genus surfaces have many isospectral hyperbolic structures.

New research finds 145 infinite families of CS spheres are standard.

Study finds infinite families of Sasaki-Einstein metrics on spheres.

Infinite families of maps found on ellipsoids in various dimensions.

The author, in her previous paper, constructed an infinite family of 3-bridge links each of which admits infinitely many 3-bridge spheres up to isotopy. In this paper, we prove that if a prime, unsplittable link $L$ in $S^3$ admits infinitely many 3-bridge spheres up to isotopy then $L$ belongs to the family.

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial…

We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

The paper analyzes the Rashomon ratio for infinite classifier families and shows its importance for choosing good classifiers.

In this note, we classify Stein fillings of an infinite family of contact 3-manifolds up to diffeomorphism. Some contact 3-manifolds in this family can be obtained by Legendrian surgeries on $(S^3,ξ_{std})$ along certain Legendrian 2-bridge knots. We also classify Stein fillings, up to symplectic deformation, of an inf…

In this article we determine, for an infinite family of maps on the plane, the topology of the surface on which the minimal regular covering occurs. This infinite family includes all Archimedean maps.

New infinite families of flat spaces found from symmetric spaces.

New families of hyperbolic polyhedra yield infinitely many unique reflection groups.

Study finds infinite non-fibered twisted torus knots.

In this note, we exhibit infinite families of tight non-fillable contact manifolds supported by planar open books with vanishing Heegaard Floer contact invariants. Moreover, we also exhibit an infinite such family where the supported manifold is hyperbolic.

Generalising the results in arXiv:1612.00281, we construct infinite-dimensional families of non-singular stationary space times, solutions of Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations with a negative cosmological constant. The families include an infinite-dimensional family of soluti…

A state generating is introduced to determine the Jones polynomial of a link. Formulae for two infinite families of knots are shown by applying this method, the second family of which are proved to be non-alternating. Moreover, the method is generalized to compute the Jones-Kauffman polynomial of a virtual link. As exa…

New infinite family of hyperbolic L-space knots with specific semigroups.

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how these tori can be non-isotopically embedded as homologous symplectic …

Researchers found infinitely many non-collapsed steady Ricci solitons on complex line bundles.

We construct several infinite families of nonnegatively curved manifolds of low cohomogeneity and small dimension which can be distinguished by their cohomology rings. In particular, we exhibit an infinite family of eight-dimensional cohomogeneity one manifolds of nonnegative curvature with pairwise non-isomorphic comp…

Starting with the Dolgachev surface E(1)_{2,3} we construct an infinite family of distinct exotic copies of the rational surface E(1), each of which admits a handlebody decomposition without 1- and 3- handles, and we draw these handlebodies.

We introduce a general procedure called `reverse engineering' that can be used to construct infinite families of smooth 4-manifolds in a given homeomorphism type. As one of the applications of this technique, we produce an infinite family of pairwise nondiffeomorphic 4-manifolds homeomorphic to CP^2#3(-CP^2).

We construct a new infinite family of models of exotic 7-spheres. These models are direct generalizations of the Gromoll-Meyer sphere. From their symmetries, geodesics and submanifolds half of them are closer to the standard 7-sphere than any other known model for an exotic 7-sphere.

For any integer $n\geq 2$, we construct an infinite family of Stein fillable contact $(4n-1)$-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.

We construct an infinite family of quasi-alternating links from a given quasi-alternating link by replacing a crossing by a product of rational tangles each of which extends that crossing. Consequently, we determine an infinite family of quasi-alternating Montesinos links. This family contains all the classes of quasi-…

In this preliminary work, we study the generalization properties of infinite ensembles of infinitely-wide neural networks. Amazingly, this model family admits tractable calculations for many information-theoretic quantities. We report analytical and empirical investigations in the search for signals that correlate with…

Classifies knot traces with specific trisection genus limits.

An infinite family of pairwise nonhomeomorphic 13-dimensional positively curved manifolds is constructed

The paper finds virtual knots with specific unknotting indices.

The paper resolves conjectures about knot invariants and shows infinite families of knots.

The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric …

In this note we construct infinitely many distinct simply connected Stein fillings of a certain infinite family of contact 3--manifolds.

Paper finds first examples of unlinked knots that can't be separated.

Infinite family of hyperbolic 3-manifolds with large volumes.

Suppose that $X,X'$ are simply-connected closed exotic 4-manifolds. It is well-known that $X'$ is obtained by an order 2 cork twist of $X$. We give an infinite exotic family of 4-manifolds not generated by any infinite order cork. This is the first example admitting such a condition. We prove a necessary condition of 4…

We study families of Galois covers of curves of positive genus. It is known that under a numerical condition these families yield Shimura subvarieties generically contained in the Jacobian locus. We prove that there are only 6 families satisfying this condition, all of them in genus 2,3 or 4. We also show that these fa…

Study shows infinite families of manifolds with nonnegative curvature.

We found an infinite family of counterexamples to Batson's conjecture.

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equa…

We describe a family of 4-dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic 24-cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of the isometry…

There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this paper we show that free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible 4-manifold. We give a new infinite family of examples in which …

This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…