arXiv research

The study finds infinitely many different geometries for odd-dimensional manifolds with positive Ricci curvature.

Accessible groups with infinitely many ends have infinitely many twisted conjugacy classes.

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…

Veech groups uniformize Teichmüller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely many cusps and infinitely many infinite ends. We further show that examples exist for which each direction of an infinite end …

Positive braids have endless filling possibilities.

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.

We prove that all maximal-tb Legendrian torus links (n,m) in the standard contact 3-sphere, except for (2,m),(3,3),(3,4) and (3,5), admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances which induce faithful actions of the modu…

3-manifolds have covers with infinitely many ideal triangulations.

In this article we present infinitely many 3-manifolds admitting infinitely many universally tight contact structures each with trivial Ozsvath-Szabo contact invariants. By known properties of these invariants the contact structures constructed here are non weakly symplectically fillable.

New examples of Legendrian links with infinitely many fillings.

A manifold has infinitely many sphere fibrations over a sphere.

The paper shows infinitely many components in Floer Hessians space.

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.

This paper considers "geometric" ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. As far as we know, this is the first construction of infinitely man…

We prove the existence of nonperiodic, properly embedded minimal surfaces in $\mathbb{R}^2\times\mathbb{S}^1$ with genus zero, infinitely many ends and one limit end (in particular, they have infinite total curvature).

Study confirms infinitely many non-characterizing slopes for various knots.

The paper finds infinitely many 4-manifolds with non-isotopic sections.

Paper constructs infinitely many tangent functors on diffeological spaces.

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

The paper constructs infinitely many surfaces with specific mean curvature.

New groups found in hyperbolic space with infinite fields of definition.

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

We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented graphs. The fundamental groups of the resulting complexes are hyperbolic, free-by-c…

We enumerate a necessary condition for the existence of infinitely many geometrically distinct, non-constant, prime closed geodesics on an arbitrary closed Riemannian manifold $M$. That is, we show that any Riemannian metric on $M$ admits infinitely many prime closed geodesics such that the energy functional $E:ΛM\to\m…

Study flip graphs for surfaces of infinite type, finding uncountably many connected components.

We prove that if a closed hyperbolic 3-manifold M contains infinitely many totally geodesic surfaces, then M is arithmetic.

Auckly gave two examples of irreducible integer homology spheres (one toroidal and one hyperbolic) which are not surgery on a knot in the three-sphere. Using Heegaard Floer homology, the authors and Karakurt provided infinitely many small Seifert fibered examples. In this note, we extend those results to give infinitel…

The paper proves infinitely many strong symplectic fillings for cusp singularity links.

In a recent paper of Akhmedov, Etnyre, Mark and Smith, it was shown that there exist infinitely many contact Seifert fibered 3-manifolds each of which admits infinitely many exotic (homeomorphic but pairwise non-diffeomorphic) simply-connected Stein fillings. Here we extend this result to a larger set of contact Seifer…

We show that in each dimension $n\ge 10$ there exist infinite sequences of homotopy equivalent but mutually non-homeomorphic closed simply connected Riemannian $n$-manifolds with $0\le \sec\le 1$, positive Ricci curvature and uniformly bounded diameter. We also construct open manifolds of fixed diffeomorphism type whic…

Infinite knots have non-integer trace values.

Study Euler class of surface bundles with nontrivial results.

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has infinitely many leaf-wise intersection points. Moreover, any Stein …

Paper constructs infinitely many non-braid positive hyperbolic L-space knots.

We construct the first examples of manifolds, the simplest one being the product of S^3, S^4, and R^5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls.

Let C be a real-analytic Jordan curve in $R^3$. Then C cannot bound infinitely many disk-type minimal surfaces which provide relative minima of area.

New contact manifolds with many fillings found.

We show that any two non-conjugate points on a forward or backward complete connected Finsler manifold can be joined by infinitely many geodesics which are not covered by finitely many closed ones, provided that the Betti numbers of the based loop space grow unbounded.

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

New examples of manifolds with positive scalar curvature and infinitely many poles.

New knots bound multiple non-isotopic ribbon disks.

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

The paper explores smooth equivariant rigidity and finds infinitely many exotic smooth structures.

The paper constructs infinitely many stably diffeomorphic but non-homotopy equivalent manifolds.

New examples of knots with infinitely many inequivalent slice disks.

Study finds infinitely many surface bundle types with zero signature.

Certain torus knots have infinitely many slopes that do not uniquely identify them.

Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.