# Tagged Questions

**10**

votes

**3**answers

336 views

### Take contraction wrt a vector field twice and define kernel mod image. Does that give anything interesting?

I apologize in advance if this question is too vague for mathoverflow. My main aim is to get some references for a concept.
First, we make the following observation: let $X: M \rightarrow TM $ be a ...

**1**

vote

**1**answer

356 views

### When do submanifolds lie in the same homology class? [closed]

Hello,
this may be a trivial question, but I am not very familiar with the topic.
Let (M,g) be a Riemannian Manifold. (In fact, we don't need the metric here.)
What exactly does it take for two ...

**1**

vote

**1**answer

308 views

### When is there a deRham duality relation between the fundamental class and a top form.?

Hi, everyone:
I am reading a small expository paper on properties of CP2,
in which the intersection form is defined as an integral of
the wedge of two forms $w_1$, $w_2$, and these forms ...

**4**

votes

**2**answers

1k views

### De Rham homology

Suppose M is an arbitrary smooth manifold and D is its bundle of 1-densities.
On the category of finite-dimensional vector bundles over M and linear differential operators between them
there is a ...

**9**

votes

**6**answers

2k views

### CW-structures and Morse functions: a reference request

The following is probably well known, but I wasn't able to locate a reference in the literature.
Let $f$ be a Morse function on a smooth compact manifold $M$ without boundary and let $\rho$ be a ...