Cohomology of n-sphere minus k discs
1
If $M=S_n backslash K$, where $K$ is the union of $kgeq1$ disjoint disks $D_i$, how would you compute the de Rham cohomology of $M$?
differential-topology homology-cohomology smooth-manifolds differential-forms
asked Nov 27 at 0:48
mr11
161
add a comment |
1
If $M=S_n backslash K$, where $K$ is the union of $kgeq1$ disjoint disks $D_i$, how would you compute the de Rham cohomology of $M$?
differential-topology homology-cohomology smooth-manifolds differential-forms
asked Nov 27 at 0:48
mr11
161
1
By induction using the Mayer-Vietoris sequence.
– Charlie Frohman
Nov 27 at 0:55
That's actually exactly my problem. I'm self-studying smooth manifolds, and I'm not sure I have a grasp on computations using the Mayer-Vietoris sequence.
– mr11
Nov 27 at 1:48
Start by removing points from the plane so you can see how to decompose it. Remember removing the first point from $S^2$ gives the plane.
– Charlie Frohman
Nov 27 at 2:47
add a comment |
1
1
1
If $M=S_n backslash K$, where $K$ is the union of $kgeq1$ disjoint disks $D_i$, how would you compute the de Rham cohomology of $M$?
differential-topology homology-cohomology smooth-manifolds differential-forms
asked Nov 27 at 0:48
mr11
161
If $M=S_n backslash K$, where $K$ is the union of $kgeq1$ disjoint disks $D_i$, how would you compute the de Rham cohomology of $M$?
differential-topology homology-cohomology smooth-manifolds differential-forms
differential-topology homology-cohomology smooth-manifolds differential-forms
asked Nov 27 at 0:48
mr11
161
asked Nov 27 at 0:48
mr11
161
asked Nov 27 at 0:48
mr11
161
asked Nov 27 at 0:48
mr11
161
asked Nov 27 at 0:48
mr11
161
161
1
By induction using the Mayer-Vietoris sequence.
– Charlie Frohman
Nov 27 at 0:55
That's actually exactly my problem. I'm self-studying smooth manifolds, and I'm not sure I have a grasp on computations using the Mayer-Vietoris sequence.
– mr11
Nov 27 at 1:48
Start by removing points from the plane so you can see how to decompose it. Remember removing the first point from $S^2$ gives the plane.
– Charlie Frohman
Nov 27 at 2:47
add a comment |
1
By induction using the Mayer-Vietoris sequence.
– Charlie Frohman
Nov 27 at 0:55
That's actually exactly my problem. I'm self-studying smooth manifolds, and I'm not sure I have a grasp on computations using the Mayer-Vietoris sequence.
– mr11
Nov 27 at 1:48
Start by removing points from the plane so you can see how to decompose it. Remember removing the first point from $S^2$ gives the plane.
– Charlie Frohman
Nov 27 at 2:47
1
1
By induction using the Mayer-Vietoris sequence.
– Charlie Frohman
Nov 27 at 0:55
By induction using the Mayer-Vietoris sequence.
– Charlie Frohman
Nov 27 at 0:55
That's actually exactly my problem. I'm self-studying smooth manifolds, and I'm not sure I have a grasp on computations using the Mayer-Vietoris sequence.
– mr11
Nov 27 at 1:48
That's actually exactly my problem. I'm self-studying smooth manifolds, and I'm not sure I have a grasp on computations using the Mayer-Vietoris sequence.
– mr11
Nov 27 at 1:48
Start by removing points from the plane so you can see how to decompose it. Remember removing the first point from $S^2$ gives the plane.
– Charlie Frohman
Nov 27 at 2:47
Start by removing points from the plane so you can see how to decompose it. Remember removing the first point from $S^2$ gives the plane.
– Charlie Frohman
Nov 27 at 2:47
add a comment |
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1
By induction using the Mayer-Vietoris sequence.
– Charlie Frohman
Nov 27 at 0:55
That's actually exactly my problem. I'm self-studying smooth manifolds, and I'm not sure I have a grasp on computations using the Mayer-Vietoris sequence.
– mr11
Nov 27 at 1:48
Start by removing points from the plane so you can see how to decompose it. Remember removing the first point from $S^2$ gives the plane.
– Charlie Frohman
Nov 27 at 2:47