Smooth parameterization inside a manifold factors through the inclusion of a submanifold?











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I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.



My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?










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    up vote
    0
    down vote

    favorite












    I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.



    My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?










    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.



      My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?










      share|cite|improve this question













      I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.



      My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?







      differential-geometry






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      share|cite|improve this question










      asked Nov 20 at 20:53









      D_S

      13.2k51551




      13.2k51551



























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