Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Extending Differential Forms so That they are Globally Non-zero.
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
gk@gmail.com

Posts: 134
Registered: 11/12/12
Extending Differential Forms so That they are Globally Non-zero.
Posted: Feb 18, 2013 2:49 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Hi, All:

Let M be a smooth manifold and let w be a form defined locally only,

i.e., w is defined in individual charts.

There is a way of extending w from the local charts to the whole manifold

using a bump function f and partitions of unity; we choose a triple K,V,U

with K compact, V closed, U open, K<V<U , so that f ==1 on V , and f is 0

outside of U . Then , for each chart we patch together f.w into a global

form using partitions of unity (assume M is paracompact , so that P.O.U's

exist ). **NOW** the problem is that in this extension, w will be zero.

Question: under what conditions can we extend w into a global _non-zero_

form?

Thanks.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.