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Submersion and fiber bundles

  1. Jun 6, 2009 #1
    How would one go about to construct a function on (smooth) manifolds that is a submersion without being (the projection map of) a fiber bundle?
     
  2. jcsd
  3. Jun 12, 2009 #2
    The simplest way is to take any old map and remove the set of critical points.
     
  4. Aug 11, 2009 #3
    there are a zillion ways.

    E.G.

    Any smooth diffeomorphism is a submersion. In any manifold there is a diffeomorphism that maps any point to any other. So the list of submersions is large.

    If you don't want to use the whole manifold excise a small ball around any point and use the inclusion map . The process works for finitely many excised balls.

    The are a zillion other ways as well.
     
    Last edited: Aug 11, 2009
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