[spr] Re: Nonuniqueness of actions

Squark wrote:
>
> Hold on, though. According to what you're saying, you get a
> complex line bundle with transition functions taking values in
> {1, -1}. Such a bundle has to be trivial since I can continuously
> deform it into the trivial bundle by replacing -1 with exp(i phi) in
> the transition functions and varying phi from pi to 0.
>

Whether the structure group acting on a fibre can be made continuous or not
does not mean the bundle is trivial. In fact {1,-1} is precisely the fibre
of the Moebius band - one of the simplest non-trivial bundles. What matters
is whether you have global sections.

regards
pg