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Relation between codifferential and boundary operator

  1. Jul 18, 2008 #1
    As we know,the codifferential [tex] \delta [/tex] is the adjoint of the exterior derivative,and the boundary operator [tex] \partial [/tex] is also the adjoint of exterior derivative according to stokes' theorem, then what is the relation between codifferential and boundary operator?
     
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  3. Jul 19, 2008 #2

    HallsofIvy

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    ?? The only relation is exactly what you have given: Stoke's theorem.
     
  4. Jul 20, 2008 #3
    Stokes' theorem states that [tex] <D,d \omega >=<\partial D,\omega> [/tex] ([tex] \partial [/tex] is the boundary operator), exterior derivative d and codifferential [tex] \delta [/tex] hold the relation [tex] (\theta ,d \omega)=(\delta \theta ,\omega) [/tex],then could we form a formula between [tex] \partial [/tex] and [tex] \delta [/tex] directly?
     
  5. Jul 20, 2008 #4

    HallsofIvy

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    No, they are completely different things. In fact, it really does not make sense to talk about "d" without the [itex]\omega[/itex] or [itex]\delta[/itex] with out the [itex]\theta[/itex].
     
  6. Aug 24, 2008 #5
    So B=Dual(A) and C=Dual(A) do not imply B=C, right? I once thought that the dual of one object must be unique, it is not true?
     
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