We prove an embedding theorem for maps from a finite complex into a Poincaré duality space. The proof uses fiberwise homotopy theory.

We prove a categoricity transfer theorem for tame abstract elementary classes. Theorem 0.1. Suppose that K is a χ-tame abstract elementary class and satisfies the amalgamation and joint embedding properties and has arbitrarily large models. Let λ ≥ Max{χ,LS(K)}. If K is categorical in λ and λ, then K is categorical in λ. Combining this theorem with some results from [Sh 394], we derive a form o...

The classical Sobolev embedding theorem of the space of functions of bounded variation BV (Rn) into Ln (Rn) is proved in a sharp quantitative form.

We consider several ways to measure the ‘geometric complexity’ of an embedding from a simplicial complex into Euclidean space. One of these is a version of ‘thickness’, based on a paper of Kolmogorov and Barzdin. We prove inequalities relating the thickness and the number of simplices in the simplicial complex, generalizing an estimate that Kolmogorov and Barzdin proved for graphs. We also cons...

Let H be a fixed graph. What can be said about graphs G that have no subgraph isomorphic to a subdivision of H? Grohe and Marx proved that such graphs G satisfy a certain structure theorem that is not satisfied by graphs that contain a subdivision of a (larger) graph H1. Dvořák found a clever strengthening—his structure is not satisfied by graphs that contain a subdivision of a graph H2, where ...

A famous theorem due to Nash ([3]) assures that every Riemannian manifold can be embedded isometrically into some Euclidean space E. An interesting question is whether for a complete manifold M we can find a closed isometric embedding. This note gives the affirmative answer to this question asked to the author by Paolo Piccione. In his famous 1956 article John Nash proved that every Riemannian ...

A theorem of Mislin gives an equivalence between a condition on restriction of cohomology to a subgroup with an embedding condition on the subgroup. Two variations of this result are proved and a reduction is given towards a purely algebraic proof of Mislin’s original theorem. © 2005 Elsevier B.V. All rights reserved.

We present a new embedding theorem for time series, in the spirit of Takens's theorem, but requiring multivariate signals. Our result is part of a growing body of work that extends the domain of geometric time series analysis to some genuinely stochastic systems|including such natural examples as xj+1 = (xj) + j where is some xed map and the j are i.i.d. random displacements.