# Tagged Questions

**2**

votes

**1**answer

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**

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**0**answers

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

**1**answer

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 ...