Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Regular Point Theorem of Manifolds with Boundaries

  1. Apr 11, 2012 #1
    Dear Folks:
    In most textbooks on differential geometry, the regular theorem states for manifolds without boundaries: the preimage of a regular value is a imbedding submanifold. What about the monifolds with boundaries??
    Many Thanks!!
     
  2. jcsd
  3. Apr 11, 2012 #2

    lavinia

    User Avatar
    Science Advisor
    Gold Member

    I passionately recommend Milnor's book, Topology from the Differentiable Viewpoint which covers this and many other topics in Differential Topology.

    The regular value theorem is an application of the Implicit Function Theorem. Extending it to a manifold with boundary is a good exercise.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Regular Point Theorem of Manifolds with Boundaries
  1. Manifold with Boundary (Replies: 7)

Loading...