2
votes
1answer
281 views

Contractibility of a configuration space

For a topological space $X$ and a positive integer $k\in \mathbb{N}_{>0}$ let $F_k(X):= \{ (x_1,\ldots,x_k)\in X^k |x_i\neq x_j \text{ for } i\neq j \}$ be its $k$-configuration space. Let ...
4
votes
0answers
290 views

Calculate the cohomology ring using Morse Theory [closed]

My question is: Is there any way to calculate the cohomology ring of a finite dimension manifold using the Morse theory? The cohomology ring structure strongly rely on the following things ...
3
votes
1answer
431 views

Morse theory and adiabatic limits

Let's start with a product manifold $M\times N$, with a product Riemannian metric $g_M\oplus g_N$. Consider a generic Morse function $f(x, y)$ on $M\times N$. Then its critical points are discrete and ...