Regular Point Theorem of Manifolds with Boundaries

[Fangyang Tian]

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!

 

[lavinia]

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!

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.