Twisted forms and intuition.

bmegun

Can anyone suggest insight, or a course of study, that can improve understanding of twisted (or pseudo) forms. I have learned from reading Frankel and Burke, that half the forms used in physical theory are twisted, and though I've studied their chapters on the subject, my intuition is still inadequate. It seems so strange to have developed an elaborate theory of intrinsic geometric objects (forms) and to then introduce a vestige of a coordinate system, by introducing orientation. Though Burke indicates that neither twisted or ordinary forms are more fundamental, I have not seen an intrisic definition of twisted forms. In any case, I would like to improve
my understanding and intuition, through simple examples, and or a reading
list.

robphy

I have also been trying to develop my intuition about twisted forms.

Have you already seen
(Burke) Twisted Forms as they should be ?

Here is a list of some references that may be helpful.
physics.syr.edu/courses/vrml/electromagnetism/references.html

Additionally, (Bossavit) Applied differential geometry may be useful.