Related papers: Intersection forms of almost-flat 4-manifolds

We present a topological recursion formula for calculating the intersection numbers defined on the moduli space of open Riemann surfaces. The spectral curve is $x = \frac{1}{2}y^2$, the same as spectral curve used to calculate intersection…

We show that if a simply connected manifold is almost quarter pinched then it is diffeomorphic to a CROSS (a compact rank one symmetric space) or a sphere.

Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic…

Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-K\"ahler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized…

For any simple digraph $D$ we offer a new proof for the intersection number of its middle digraph, $M(D)$; while doing so we also solve for the intersection number when $D$ has loops. In addition, a new transformation, the union of $D$ and…

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.

We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces.…

The Riemann-Wirtinger integral is an analogue of the hypergeometric integral, which is defined as an integral on a one-dimensional complex torus. We study the intersection forms on the twisted homology and cohomology groups associated with…

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…

We give an explicit formula for the self-intersection number of negative curves on Fermat surfaces. The formula offers us hints to either prove or disprove the Bounded Negativity Conjecture for the Fermat surfaces.

We study strong approximation for the intersection of two affine quadrics. As its application, we prove the fibration method for weak approximation over number fields of rank four with nonsplit fibers split by quadratic extensions.

We find an algorithm to compute the quadratic Euler characteristic of a smooth projective complete intersection of hypersurfaces of the same degree. As an example, we compute the quadratic Euler characteristic of a smooth projective…

The intersection graph $\Delta_G$ of a finite group $G$ is a simple graph with vertices the non-trivial proper subgroups of $G$, and an edge between two vertices if their corresponding subgroups intersect non-trivially. These graphs were…

We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product $Y \times Y'$ and…

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface $X\subset \bbP^{4}$ of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type…

Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,\omega)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the…

We calculate Perelman's invariant for compact complex surfaces and a few other smooth four-manifolds. We also prove some results concerning the dependence of Perelman's invariant on the smooth structure.

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.

A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms.

In this note, we first bound the intersection number of the regular simplicial partitions.