Related papers: Six-dimensional GKM manifolds with four fixed poin…

This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of…

We consider stable manifolds of a holomorphic diffeomorphism of a complex manifold. Using a conjugation of the dynamics to a (non-stationary) polynomial normal form, we show that typical stable manifolds are biholomorphic to complex…

Consider a curve $\Gamma$ in a domain $D$ in the plane $\boldsymbol R^2$. Thinking of $D$ as a piece of paper, one can make a curved folding $P$ in the Euclidean space $\boldsymbol R^3$. The singular set $C$ of $P$ as a space curve is…

In this note we prove that, for any integer n, there exist a smooth 4-manifold, homotopic to a K3 surface, defined by applying the link surgery method of Fintushel-Stern to a certain 2-component graph link, which admits n inequivalent…

A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of…

Following the recent exploration of smooth heterotic compactifications with unitary bundles, orbifold compactifications in six dimensions can be shown to correspond in the blow-up to compactifications with U(1) gauge backgrounds. A powerful…

One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one can enumerate all rigid positive semidefinite quadratic…

In the author's earlier work there appeared a new way to specify any smooth closed 4-manifold by a surface diagram, which consists of an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each…

We consider the action of the group $\mathrm{PGL}_4(K)$ on the smooth cubic surfaces of $\mathbb{P}^3_K$ ($K$ an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with non…

We present a computational study of smooth curves of degree six in the real projective plane. In the Rokhlin-Nikulin classification, there are 56 topological types, refined into 64 rigid isotopy classes. We developed software that…

We will define a version of Seiberg-Witten-Floer stable homotopy types for a closed, oriented 3-manifold $Y$ with $b_1(Y) > 0$ and a spin-c structure $\mathfrak{c}$ on $Y$ with $c_1(\mathfrak{c})$ torsion under an assumption on $Y$. Using…

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

We show the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a quotient manifold of $\mathbb{S}^{n-1}\times \mathbb{R}$…

There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable $\mathcal{G}_1,\dots,\mathcal{G}_6$ and four are non-orientable $\mathcal{B}_1,\dots,\mathcal{B}_4$. In the present paper we investigate…

In this paper, we classify simply connected closed smooth $13$-dimensional manifolds whose cohomology ring is isomorphic to that of $\mb{CP}^3\times S^7$, up to diffeomorphism, homeomorphism, and homotopy equivalence. Furthermore, if such a…

The present paper finds new necessary and sufficient conditions for $6$-dimensional closed and simply-connected manifolds of certain classes to admit special generic maps into certain Euclidean spaces. The class of special generic maps…

Let $M$ be a real-analytic connected CR-hypersurface of CR-dimension $n>0$ having a point of Levi-nondegeneracy. The following alternative is demonstrated for both the symmetry algebra $s$ and the automorphism group $G$ of $M$. Denote by…

We prove that in dimensions not equal to 4, 5, or 7, the homology and homotopy groups of the classifying space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses…

In dimension 4, we extend the correspondence between compact nonsingular toric varieties and regular fans to a correspondence between almost complex torus manifolds and families of multi-fans in a geometric way, where an (almost) complex…

We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physically lead to enhanced gauge…