Related papers: Van Kampen-Flores theorem and Stiefel-Whitney clas…

Let $\mathscr{C}$ be a $(d+2)$-angulated category with $d$-suspension functor $\Sigma^d$. Our main results show that every Serre functor on $\mathscr{C}$ is a $(d+2)$-angulated functor. We also show that $\mathscr{C}$ has a Serre functor…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

In this note we analyse the issue of moduli stabilisation in 4d models obtained from heterotic string compactifications on manifolds with SU(3) structure with standard embedding. In order to deal with tractable models we first integrate out…

For a given manifold $M$ we consider the non-linear Grassmann manifold $Gr_n(M)$ of $n$-dimensional submanifolds in $M$. A closed $(n+2)$-form on $M$ gives rise to a closed 2-form on $Gr_n(M)$. If the original form was integral, the 2-form…

In $(d+1)$-dimensional $1$-form nonabelian gauge theories, we classify nontrivial $0$-form bundles in $ \mathbb{R}^{d} $, which yield configurations of $D(d-2j)$-branes wrapping $(d-2j)$-cycles $c_{d-2j} $ in $Dd$-branes. We construct the…

A $d$-dimensional invertible topological field theory is a functor from the symmetric monoidal $(\infty,n)$-category of $d$-bordisms (embedded into $\mathbb{R}^\infty$ and equipped with a tangential $(X,\xi)$-structure) which lands in the…

We wish to draw attention to an interesting and promising interaction of two theories. On the one hand, it is the theory of \textbf{pseudo-triangulations} which was useful for implicit solution of thecarpenter's rule problem and proved…

We show that under certain conditions, a nontrivial Riemannian submersion from positively curved four manifolds does not exist. This gives a partial answer to a conjecture due to Fred Wilhelm. We also prove a rigidity theorem for Riemannian…

One step towards realistic Kaluza-Klein[like] theories and a loop hole through the Witten's "no-go theorem" is presented for cases which we call an effective two dimensionality cases: In $d=2$ the equations of motion following from the…

We fix an orientation issue which appears in our previous paper about the isomorphism between Floer homology of cotangent bundles and loop space homology. When the second Stiefel-Whitney class of the underlying manifold does not vanish on…

We study lower bounds for the number of vertices in a PL-triangulation of a given manifold $M$. While most of the previous estimates are based on the dimension and the connectivity of $M$, we show that further information can be extracted…

As we known, the {\it Seifert-Van Kampen theorem} handles fundamental groups of those topological spaces $X=U\cup V$ for open subsets $U, V\subset X$ such that $U\cap V$ is arcwise connected. In this paper, this theorem is generalized to…

In 1984, Dancis proved that any $d$-dimensional simplicial manifold is determined by its $(\lfloor d/2 \rfloor + 1)$-skeleton. This paper adapts his proof to the setting of cubical complexes that can be embedded into a cube of arbitrary…

We prove Wadsley's theorem for foliations by closed non-lightlike geodesics. As an application we show that every pseudo-Riemannian and non-Riemannian 2-mainfold, all of whose time- or spacelike geodesics are closed, is diffeomorphic to…

Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplexwise linear embedding of the triangulation into euclidean space is "as convex as possible". It can thus be understood as a generalization of…

Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex…

The topological Tverberg theorem states that any continuous map of a $(d+1)(r-1)$-simplex into the Euclidean $d$-space maps some points from $r$ pairwise disjoint faces of the simplex to the same point whenever $r$ is a prime power. We…

The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on…

We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…