1
vote
1answer
355 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
1answer
305 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 ...
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2answers
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
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6answers
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 ...