Related papers: Lifting generic maps to embeddings. Triangulation …

The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces into $\mathbb{R}^3$. We conclude that their proof does not admit a direct extension to…

We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichm\"uller space, we consider whether they are quasi-isometric embeddings with respect to…

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds…

Given a simplicial complex $K$, we consider several notions of geometric complexity of embeddings of $K$ in a Euclidean space ${\mathbb R}^d$: thickness, distortion, and refinement complexity (the minimal number of simplices needed for a PL…

Let $K$ be a $k$-dimensional simplicial complex having $n$ faces of dimension $k$, and $M$ a closed $(k-1)$-connected PL $2k$-dimensional manifold. We prove that for $k\ge3$ odd $K$ embeds into $M$ if and only if there are $\bullet$ a…

It is a classical important problem of differential topology by Thom; for a homology class of a compact manifold, can we realize this by a closed submanifold with no boundary? This is true if the degree of the class is smaller or equal to…

The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…

In this paper, we study the embedded topology of smooth plane quartics and its bitangent lines via two-graphs and apply it to construct interesting examples for Zariski $m$-ple.

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle…

We prove the following regularity result: If M and M' are smooth generic submanifolds of C^N and C^N' respectively, where N and N' are not necessarily equal, and if M is minimal, then every C^k-CR-map from M into M^\prime which is…

We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudo-triangulation. This generalizes the main result of math.CO/0307347 which treats the minimally generically rigid case. The proof…

Let $\imath: M\to \RR^{p+2}$ be a smooth embedding from a connected, oriented, closed $p$-dimesional smooth manifold to $\RR^{p+2}$, then there is a spin structure $\imath^\sharp(\varsigma^{p+2})$ on $M$ canonically induced from the…

We show that every locally flat topological embedding of a 3-manifold in a smooth 5-manifold is homotopic, by a small homotopy, to a smooth embedding. We deduce that topologically locally flat concordance implies smooth concordance for…

Let M and N be smooth manifolds. For an open V of M let emb(V,N) be the space of embeddings from V to N. By results of Goodwillie and Goodwillie-Klein, the cofunctor V |--> emb(V,N) is analytic if dim(N)-dim(M) > 2. We deduce that its…

If $\mathcal E, \mathcal F$ are vector bundles of ranks $r-1,r$ on a smooth fourfold $X$ and $\mathcal{Hom}(\mathcal E,\mathcal F)$ is globally generated, it is well known that the general map $\phi: \mathcal E \to \mathcal F$ is injective…

It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the orientable and smooth category, we determine the smallest possible $m$ when $n\geq 3g$.…

Let $Z$ be a smooth compact $(n+1)$-manifold. We study smooth embeddings and immersions $\beta: M \to Z$ of compact or closed $n$-manifolds $M$ such that the normal line bundle $\nu^\beta$ is trivialized. For a fixed $Z$, we introduce an…

In this note we show that a weakly geometrically flat map $\pi$ : M $\rightarrow$ N between pure dimensional complex spaces has the local lifting property for cycles. From this result we also deduce that, under these hypotheses, several…

We study embeddings between generalised Triebel-Lizorkin-Morrey spaces ${\mathcal E}^{s}_{\varphi,p,q}({\mathbb R}^d)$ and within the scales of further generalised Morrey smoothness spaces like ${\mathcal N}^{s}_{\varphi,p,q}({\mathbb…

We show that every continuous map from one translationally finite tiling space to another can be approximated by a local map. If two local maps are homotopic, then the homotopy can be chosen so that every interpolating map is also local.