## Obstructions to symplectically embedding compact manifolds of dimension 44 or higher

It is known in Li’s paper (http://arxiv.org/pdf/0812.4929v1.pdf) that in compact symplectic manifolds (X2n,ω) of dimension at least 2n≥4, an immersed symplectic surface represents a 2-homology class as long as that homology class has positive symplectic area. When 2n≥6, this immersion may even be taken to be an embedding. My question regards finding symplectically embedded submanifolds … Read more

## Amalagamation of a sequence of closed immersions of schemes

Let (Xn)n≥0 be a family of schemes. Let X0→X1→X2→… be a sequence of closed immersions (which therefore gives rise to an ind-scheme). Under which (necessarly and/or sufficient) conditions is there a scheme S and a family of closed immersions Xn→S such that Xn⟶Xn+1↘↙S commutes? This is not always satisfied (see the comments). Answer AttributionSource : … Read more

## Whitney-like embedding theorem for posets?

The Whitney embedding theorem says that any finite-dimensional smooth manifold can be embedded into $\mathbb{R}^n$ for some $n$. Is anything like this true for posets? I’m looking for conditions on a poset $P$, under which there exists an embedding of $P$ into a cube $L^n$ for some linear order $L$. I’m interested in both the … Read more

## Generalizations of Abhyankar-Moh theorem (embeddings of the line in the plane)

Abhyankar-Moh theorem says that if L is a complex line in the complex affine plane C2, then every embedding of L into C2 extends to an automorphism of the plane. It seems that one can replace C by any algebraically closed field k of characteristic zero. Are there ‘similar’ results for fields other than k, … Read more

## Generalization of Gagliardo-Nirenberg Inequality

The standard Gagliardo-Nirenberg Inequality is ‖u‖Lnn−1(Rn)≤Cn‖∇u‖L1(Rn), and constitutes a key step to proving Sobolev Injection Theorems. Of course we may assume that u is smooth and compactly supported, the important point is that the constant Cn is dimensional and independent of u. Question 1. Are there some improvements of (∗) where the rhs is replaced … Read more

## Is a Morse function always the height function of some embedding? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for MathOverflow. Closed 7 years ago. Improve this question Pictures in introductory texts to Morse theory are often drawn as to interpret a Morse function as a height function. Typically, an embedding of … Read more

## Equivariant isometric embedding of manifolds in a Hilbert space under a noncompact group action

Given a Riemannian manifold M and a group of isometries G of M, I am interested in when there exists a isometric embedding ι:M→H, where H is a Hilbert space and a representation ρ:G→B(H;H) such that for each g∈G and x∈M, ι(g(x))=ρ(g)ι(x). When M is a compact manifold and G is a compact Lie group … Read more

## Theoretical justification of time-series forecasting using Takens’ embedding

This is a cross-posting where I couldn’t get an answer. In the meantime I have tried to improve the original logic: As in Takens original paper about his embedding theorem, consider a compact m-dimensional manifold M and a smooth map f:xt∈M→xt+1∈M that expresses the state-evolution in a discrete-time state-space system. Consider a second. continuous map … Read more