Cohomology of n-sphere minus k discs











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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 $M$?










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    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















up vote
1
down vote

favorite












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 $M$?










share|cite|improve this question


















  • 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













up vote
1
down vote

favorite









up vote
1
down vote

favorite











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 $M$?










share|cite|improve this question













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






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asked Nov 27 at 0:48









mr11

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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














  • 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















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