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1. • CommentRowNumber1.
   • CommentAuthorgregprice
   • CommentTimeMay 14th 2023
   • PermaLink
   Author: gregprice
   Format: MarkdownItexThis gives the idea and definition of a pseudoorientation, and the key properties related to integration. The definition is taken from [[integration of differential forms]], and the rest is largely from my reading of several of Toby's messages in the linked Usenet thread. It'd be good to add some examples, particularly with n=2 and n=3, including in the electromagnetism context where one traditionally uses a right-hand rule to conflate orientations with pseudoorientations (and 2- with 1- and pseudo- with untwisted forms). A couple of the messages in that thread had some nice examples, but I don't have the specific messages in front of me at the moment. I may return to this in the next few days to try to track those down. <a href="https://ncatlab.org/nlab/revision/pseudoorientation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/pseudoorientation">current</a>

   This gives the idea and definition of a pseudoorientation, and the key properties related to integration. The definition is taken from integration of differential forms, and the rest is largely from my reading of several of Toby’s messages in the linked Usenet thread.

   It’d be good to add some examples, particularly with n=2 and n=3, including in the electromagnetism context where one traditionally uses a right-hand rule to conflate orientations with pseudoorientations (and 2- with 1- and pseudo- with untwisted forms). A couple of the messages in that thread had some nice examples, but I don’t have the specific messages in front of me at the moment. I may return to this in the next few days to try to track those down.

   v1, current