arXiv research

The paper establishes new band width inequalities for Riemannian bands.

It is known that the only Stein filling of the standard contact structure on S^3 is B^4. In this paper, we construct simply connected exotic compact Stein 4-manifold pairs for any Betti number $b_2 \geq 1$; we do this by enlarging corks and plugs.

Modified condition proves no positive scalar curvature for enlargeable manifolds.

We define enlargeable length-structures on closed topological manifolds and then show that the connected sum of a closed $n$-manifold with an enlargeable Riemannian length-structure with an arbitrary closed smooth manifold carries no Riemannian metrics with positive scalar curvature. We show that closed smooth manifold…

Let $(M,g^{TM})$ be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and $F$ an integrable subbundle of $T M$ . Let $k^F$ be the leafwise scalar curvature associated to $g^F=g^{TM}|_F$. We show that if either $TM$ or $F$ is spin, then ${\rm inf}(k^F)\leq 0$. This gen…

We generalize the famous result of Gromov and Lawson on the nonexistence of metric of positive scalar curvature on enlargeable manifolds to the case of foliations, without using index theorems on noncompact manifolds.

New method detects foliation enlargeability.

In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the first relevant paper of Gromov and Lawson, involving contracting maps defined on …

For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this construction imply that the corresponding largeness properties of closed manifolds dep…

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras. Our proofs do not depend on the Baum--Connes conjecture and provide independent co…

We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomo…

We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold…

We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and $\partial$-reducible. A manifold in the second family has boundary consi…

Examines insurance market development and similarity post-2004 EU enlargement.

The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.

Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.

Study filling links in 3-manifolds to understand their topological properties.

Affirmative proof that rank 3 3-manifolds have filling links.

Develops a diagrammatic method for symplectic filling classifications.

If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperboli…

If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.

Infinitely many 3D shapes have multiple ways to be filled with special surfaces.

Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of th…

Gromov's universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold i…

New contact manifolds with many fillings found.

The study of symplectic fillings for rational cuspidal curves.

Develop criteria to distinguish Gromov-Thurston manifolds using algebraic Dehn fillings.

Effective drilling and filling bounds for hyperbolic 3-manifolds.

We consider a homological enlargement of the mapping class group, defined by homology cylinders over a closed oriented surface (up to homology cobordism). These are important model objects in the recent Goussarov-Habiro theory of finite-type invariants of 3-manifolds. We study the structure of this group from several d…

In this paper we state and prove a higher index theorem for an odd-dimensional connected spin riemannian manifold $(M,g)$ which is partitioned by an oriented closed hypersurface $N$. This index theorem generalizes a theorem due to N. Higson and J. Roe in the context of Hilbert modules. Then we apply this theorem to pro…

Study gives bounds on filling radius for Riemannian manifolds.

Study shows no large mean curvature fill-ins for nonnegative scalar curvature.

We show that an enlargeable Riemannian metric on a (possibly nonspin) manifold cannot have uniformly positive scalar curvature. This extends a well-known result of Gromov and Lawson to the nonspin setting. We also prove that every noncompact manifold admits a nonenlargeable metric. In proving the first result, we use t…

We prove an explicit, quantitative criterion that ensures the Heegaard surfaces in Dehn fillings behave "as expected." Given a cusped hyperbolic manifold X, and a Dehn filling whose meridian and longitude curves are longer than 2pi(2g-1), we show that every genus g Heegaard splitting of the filled manifold is isotopic …

The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.

The abstract discusses applications of Menke's JSJ decomposition to symplectic fillings of various 3-manifolds.

This paper classifies Dehn fillings of a specific 3-manifold using invariant properties.

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…

Proves upper bound on filling radius for manifolds with positive scalar curvature.

An irreducible 3--manifold with torus boundary either is a Seifert fibered space or admits at most three lens space fillings according to the Cyclic Surgery Theorem. We examine the sharpness of this theorem by classifying the non-hyperbolic manifolds with more than one lens space filling, classifying the hyperbolic man…

In this paper, we investigate the minimal symplectic fillings of small Seifert 3-manifolds with a canonical contact structure. As a result, we classify all minimal symplectic fillings of small Seifert 3-manifolds satisfying certain conditions. Furthermore, we also demonstrate that every such a minimal symplectic fillin…

We prove that simply connected open Riemannian manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.

For a hyperbolic 3-manifold $M$ with a torus boundary component,all but finitely many Dehn fillings yield hyperbolic 3-manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such situation, Gordon gave an upper bound 5 for the…

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…

Study on the number of volume-preserving Dehn fillings of hyperbolic 3-manifolds.

Study monodromy relations in Seifert fibered spaces for 3-manifold fillings.

The paper confirms a conjecture about optimal expected utility in markets with insider information.

The paper surveys mathematical results on filtration enlargement with financial examples.