Related papers: Odd-dimensional Charney-Davis conjecture
Let $\mathbb{R}^n$ be the n-dimensional Euclidean space with $O$ as the origin. Let $\wedge$ be a lattice of determinant $1$ such that there is a sphere $|X|<R$ which contains no point of $\wedge$ other than $O$ and has $n$ linearly…
Employing ideas of noncommutative geometry, certain dimensional invariant for quantum homogeneous spaces has been proposed and here we take up its computation for quaternion spheres.
We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the…
The bellows conjecture claims that the volume of any flexible polyhedron of dimension 3 or higher is constant during the flexion. The bellows conjecture was proved for flexible polyhedra in the Euclidean spaces of dimensions 3 and higher,…
We show that for an arbitrarily given closed Riemannian manifold $M$ admitting a point $p \in M$ with a single cut point, every closed Riemannian manifold $N$ admitting a point $q \in N$ with a single cut point is diffeomorphic to $M$ if…
The Manin conjecture is established for a split singular cubic surface in P^3, with singularity type D_5.
We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)
Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation properties of continuous rational maps with values in…
We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expected, as the obstruction arises in odd rather than even…
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
An open set in C^n is pseudoconvex if and only if its intersection with every affine subspace of complex dimension two as seen as an open set in C^2 is pseudoconvex.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
We give negative answers to Lin-Ni's conjecture for any four and six dimensional domains. No condition on the symmetry, geometry nor topology of the domain is needed.
We discuss some variants of cone theorem for movable curves in any codimensions.
We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two…
Sphere recognition is known to be undecidable in dimensions five and beyond, and no polynomial time method is known in dimensions three and four. Here we report on positive and negative computational results with the goal to explore the…
This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.
The existence of a "Plastikstufe" for a contact structure implies the Weinstein conjecture for all supporting contact forms.