Related papers: Diffeomorphic moment-angle manifolds with differen…

In the present paper, we introduce the notion of pseudo-heaviness of closed subsets of closed symplectic manifolds and prove the existence of pseudo-heavy fibers of moment maps. In particular, we generalize Entov and Polterovich's theorem,…

Given a multisymplectic manifold $(M,\omega)$ and a Lie algebra $\frak{g}$ acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an $L_{\infty}$-algebra-homomorphism from $\frak{g}$ to the…

In this paper, we study conjugacy invariants for 2-dimensional diffeomorphisms with homoclinic cubic tangencies (two-sided tangencies of the lowest order) under certain open conditions. Ordinary arguments used in past studies of conjugacy…

We study face numbers of simplicial complexes that triangulate manifolds (or even normal pseudomanifolds) with boundary. Specifically, we establish a sharp lower bound on the number of interior edges of a simplicial normal pseudomanifold…

We introduce Smale-Vietoris diffeomorphisms that include the classical DE-mappings with Smale solenoids. We describe the correspondence between basic sets of axiom A Smale-Vietoris diffeomorphisms and basic sets of nonsingular axiom A…

We consider simple polytopes $P=vc^{k}(\Delta^{n_{1}}\times\ldots\times\Delta^{n_{r}})$, for $n_1\ge\ldots\ge n_r\ge 1,r\ge 1,k\ge 0$, that is, $k$-vertex cuts of a product of simplices, and call them {\emph{generalized truncation…

We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped…

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…

We consider families of simple polytopes $P$ and simplicial complexes $K$ well-known in polytope theory and convex geometry, and show that their moment-angle complexes have some remarkable homotopy properties which depend on combinatorics…

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane…

We announce the discovery of a diffeomorphism of a three-dimensional manifold with boundary which has two disjoint attractors. Each attractor attracts a set of positive $3$-dimensional Lebesgue measure whose points of Lebesgue density are…

We describe the space of Poisson bivectors near a log-symplectic structure up to small diffeomorphisms.

We give necessary and sufficient conditions for a 4-manifold to be a branched covering of $CP^2$, $S^2\times S^2$, $S^2 \mathbin{\tilde\times} S^2$ and $S^3 \times S^1$, which are expressed in terms of the Betti numbers and the intersection…

The one-skeleton of a G-manifold M is the set of points p in M where $\dim G_p \geq \dim G -1$; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwitz and MacPherson show that for such a manifold this…

Two smooth manifolds M and N are called R-diffeomorphic if their product with the real line are diffeomorphic. We consider the following simplification problem: does R-diffeomorphism imply diffeomorphism or homeomorphism? For compact…

We determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on $n$ vertices.

It is known that polytopes with at most two nonsimple vertices are reconstructible from their graphs, and that $d$-polytopes with at most $d-2$ nonsimple vertices are reconstructible from their 2-skeletons. Here we close the gap between 2…

Polygon spaces like $M_\ell=\{(u_1,...,u_n)\in S^1\times... S^1 ;\ \sum_{i=1}^n l_iu_i=0\}/SO(2)$ or they three dimensional analogues $N_\ell$ play an important r\^ole in geometry and topology, and are also of interest in robotics where the…

We provide examples of contact manifolds of any odd dimension $\geq 5$ which are not diffeomorphic but have exact symplectomorphic symplectizations.

We analyze the moduli space of non-flat homogeneous affine connections on surfaces. For Type $\mathcal{A}$ surfaces, we write down complete sets of invariants that determine the local isomorphism type depending on the rank of the Ricci…