Given a regular (constant rank) bi-vector $\Pi \in \Gamma(\bigwedge^2TM)$ on a smooth manifold $M$ the necessary and sufficient condition for the image of $\Pi^\sharp:T^*M\to TM$ t …

Let ${\mathcal{G} = \lbrace s,t:G_1 \to G_0 \rbrace}$ be a Lie groupoid. Define $$(\mathcal{G}^k)_0:=\lbrace (a_1,\dots,a_k) \in G_1^k\mid s(a_1)=t(a_1)=\dots=s(a_k)=t(a_k) \rbrac …

Ekedahl wrote about foliation in characteristic positive, over the field $/frac{Z}{pZ}$ as a subsheaft of the tangent sheaft, that is closed over involution and $p$-power, My quest …

Given two smooth manifolds $M$ and $N$, it is known that if $M$ is compact, then $C^\infty(M,N)$ is a Fréchet manifold whose tangent space at $f \in C^\infty(M,N)$ is the space $$T …

I have a question about the proof of Theorem 5 in Thurston's paper "A norm for the homology of 3-manifolds". It's the theorem that asserts that the fibered faces are, well, fibere …

Recall a tranverse metric on a (regular) foliated manifold $(M,F)$ is a positive symmetric $C^\infty (M)$-bilinear form $g$ such that 1) $Ker(g_x)=T_x F$ 2) It is invariant with …

I'm trying to make an overview of the study of partial hyperbolicity and there is an interesting concept of dynamical coherence which appears there. Some call it mild (see the Thes …

It is well known that the image of a free Lie algebra action $\rho:\mathfrak{g}\to\mathfrak{X}^1(M)$ on a manifold $M$ is an integrable distribution of constant rank $(=\rm{dim}\;\ …

Suppose we are given a closed oriented 3-manifold. It is well known that taut foliations are Reebless, and if a Reebless foliation isn't taut then the leaves which don't admit a cl …

Can we characterize when a submersion $F:M \to N$ between two smooth manifolds has connected fibers? If this is too hard, what are some sufficient conditions?

hi, i have the following question: Let $M$ be a n-dimensional manifold (or riemannian or everything thats nice ...) and let $\mathcal{F}$ be a foliation of $M$ by surfaces. Assume …

Take the 3-dimensional complex projective space $\mathbb{P}^3$. Consider the action of the group $SU(2)\times SU(2)$. I have read in physics related articles that these group gives …

Consider the manifold $\mathbb{R^2}\setminus {0}$, on which the group of rotation acts. The orbits of the group are the circles centered in the origin, and form a foliation of $\ma …

Hello, I would like to obtain a smooth model around a singular point of a foliation (in my case the model should be the linearization of the foliation). It seems that the answer …

Take a smooth manifold $M^n$ with a smooth foliation $F$. Consider the sheaf $\cal F$ of $C^{\infty}$ functions on $M^n$, locally constant along the foliation $F$. What is known ab …