arXiv research

The non-vanishing conjecture implies the abundance conjecture in certain cases.

We prove the non-vanishing of the CMC flux of the boundaries of certain Riemannian manifolds with constant mean curvature.

Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.

The paper constructs metrics on compact manifolds using Aubin's deformations.

We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant of connected sums of 4-manifolds with positive first Betti number. The non-vanishing theorem enables us to find many new examples of 4-manifolds with non-trivial stable cohomotopy Seiberg-Witten invariants and it also gives a …

New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.

Study shows non-vanishing Stiefel-Whitney classes and absence of spin^C structures in certain hyperbolic manifolds.

Paper proves non-extendability of quasimorphism and non-vanishing of Reznikov's class.

Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.

In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.

Study confirms optimal bounds for group cohomology of Lie groups.

We solve Euler equations on graph manifolds, classifying steady flows with Morse-Bott Bernoulli functions.

Study non-vanishing $\ell^2$-Betti numbers for specific groups.

We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai's sutured manifold theory. It is hoped that the non-vanis…

Study shows non-abelian free groups' 4th cohomology is non-zero.

The problem on the minimal number (with respect to deformation) of intersection points of two closed curves on a surface is solved. Following the Nielsen approach, we define classes of intersection points and essential classes of intersection points, which "are preserved under deformation" and whose total number is cal…

We study the first uniformly finite homology group of Block and Weinberger for uniformly locally finite graphs, with coefficients in $\mathbb{Z}$ and $\mathbb{Z}_2$. When the graph is a tree, or coefficients are in $\mathbb{Z}_2$, a characterisation of the group is obtained. In the general case, we describe three pheno…

We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that this invariant can distinguish some links for which the ordinary Milnor invaria…

We show the non-vanishing of cohomology groups of sufficiently small congruence lattices in $SL(1,D)$, where $D$ is a quaternion division algebras defined over a number field $E$ contained inside a solvable extension of a totally real number field. As a corollary, we obtain new examples of compact, arithmetic, hyperbol…

We show that surface bundles over surfaces with base and fiber of genus at least 2 have non-vanishing simplicial volume.

We state and prove a generalization of the Poincaré-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.

We prove a non-vanishing result for the $L_{q,p}$-cohomology of complete simply-connected Riemannian manifolds with pinched negative curvature.

The study finds hyperbolic manifolds without spin^c structures in dimensions 5 and above.

We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant.

We determine the isomorphism classes of symmetric symplectic manifolds of dimension at least 4 which are connected, simply-connected and have a curvature tensor which has only one non-vanishing irreducible component -- the Ricci tensor.

The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.

The affine-additive group is hyperbolic with a non-vanishing 4-capacity.

We prove that the mean curvature $τ$ of the slices given by a constant mean curvature foliation can be used as a time function, i.e. $τ$ is smooth with non-vanishing gradient.

We construct examples of $S^1$-manifolds with finite second homotopy group and non-vanishing $\hat A$-genus. This is related to the classification of positive quaternionic Kaehler manifolds.

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are given.

New rigidity result for non-orientable manifolds with scalar curvature constraints.

We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.

We show that a compact embedded minimal or constant mean curvature annulus with non-vanishing Gaussian curvature which is tangent to two spheres of same radius or tangent to a sphere and meeting a plane in constant contact angle is rotational.

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thur…

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $κ_μ$ (relatively to a suitable riemannian metric $μ$) is zero. In the transversally orientable case…

The study explores Legendrian invariants and half Giroux torsion in contact structures.

We observe inequalities involving the Herzlich volume of a 4-dimensional asymptotically complex hyperbolic Einstein manifold and its Euler characteristic provided the metrics is either Kaehler or selfdual. In the selfdual case we have to assume furthermore that the Kronheimer-Mrowka invariant is non vanishing.

In 2001, Zhongmin Shen asked if it is possible for two projectively related Finsler metrics to have the same Riemann curvature tensor, [14, page 184]. In this paper, we provide an answer to this question, within the class of Finsler metrics of scalar flag curvature. In Theorem 3.1, we show that the answer is negative, …

We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and compute the first non-vanishing invariants of the Milnor link and of several other links. Moreover, we refine the original Milnor invariants …

We study the flux homomorphism for closed forms of arbitrary degree, with special emphasis on volume forms and on symplectic forms. The volume flux group is an invariant of the underlying manifold, whose non-vanishing implies that the manifold resembles one with a circle action with homologically essential orbits.

Study mean curvature flow in hyperbolic 3-manifolds, proving foliations and existence of minimal surfaces.

We study the homotopy type of the harmonic compactification of the moduli space of a 2-cobordism S with one outgoing boundary component, or equivalently of the space of Sullivan diagrams of type S on one circle. Our results are of two types: vanishing and non-vanishing. In our vanishing results we are able to show that…

Milnor's invariants are some of the more fundamental oriented link concordance invariants; they behave as higher order linking numbers and can be computed using combinatorial group theory (due to Milnor), Massey products (due to Turaev and Porter), and higher order intersections (due to Cochran). In this paper, we gene…

We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with $D$ independent variables. We find that the second and third cohomology groups are generically non-vanishing in $D>1$. Hence, in contrast with the $D=1$ case, the deformation theory in the multivariable case is non-trivial.

For test configurations, the Donaldson-Futaki invariant F_1 is well-known. In this note, its refinement will be discussed. Then we see that Li-Xu's pathology doesn't occur, since their example of a non-normal test configuration, with trivial normalization, actually has non-vanishing F_1 in this refined sense.

In this article we study compact Kähler manifolds $X$ admitting non-singular holomorphic vector fields with the aim of extending to this setting the classical birational classification of projective varieties with tangent vector fields. We prove that any such a Kähler manifold $X$ admits an arbitrarily small deformatio…

The contact invariant is an element in the monopole Floer homology groups of an oriented closed three manifold canonically associated to a given contact structure. A non-vanishing contact invariant implies that the original contact structure is tight, so understanding its behavior under symplectic cobordisms is of inte…

In this expository article we first give an overview on multiplier ideal sheaves and geometric problems in Kählerian and Sasakian geometries. Then we review our recent results on the relationship between the support of the subschemes cut out by multiplier ideal sheaves and the invariant whose non-vanishing obstructs th…