Is every orientation form on a compact smooth manifold closed?

In summary, when the orientation form is closed, it means that the designated time period for submitting the form has ended. In most cases, this means that the opportunity to participate has ended. To find out when the orientation form will open again, it is best to contact the organizers or check their website for updates. Some organizations may offer a notification system for when the form opens again. It is possible to attend the orientation without submitting the form, but it is not guaranteed and it is best to check with the organizers.
  • #1
robforsub
16
0
Is every orientation form w on a compact smooth manifold closed?(i.e. dw=0)
 
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  • #2
Unless I am missing something, yes, since the exterior derivative of an n-form would
be (is) an (n+1)-form in an n-manifold.
 
  • #3
Correct. It is an algebraic fact that the (n+k)-th exterior power of an n-dimensional vector space is 0 for any k>0. Since the exterior derivative of an orientation form on an n-manifold is an object of the (n+1)-th exterior power of the cotangent bundle, it is 0.
 

Related to Is every orientation form on a compact smooth manifold closed?

1. What does it mean when the "Orientation form is closed"?

When the orientation form is closed, it means that the designated time period for submitting the form has ended. This could be due to a deadline passing or the maximum number of participants being reached.

2. Can I still participate if the orientation form is closed?

In most cases, if the orientation form is closed, it means that the opportunity to participate has ended. However, it is best to check with the organizers to see if any exceptions can be made.

3. How can I find out when the orientation form will open again?

The best way to find out when the orientation form will open again is to contact the organizers or check their website for updates. They will typically announce the next available time period for submitting the form.

4. Is there a way to be notified when the orientation form opens?

Some organizations may offer a notification system for when the orientation form opens again. This could be through email, social media, or a newsletter. Check with the organizers to see if this option is available.

5. Can I still attend the orientation even if I missed the form deadline?

It is best to check with the organizers if attending the orientation without submitting the form is possible. Depending on the event or program, they may be able to make accommodations, but it is not guaranteed.

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