I'm trying to read this paper. At some point, it tries to find the minimums of an action. At first it deduces the existence of two independent solutions and says that one of them is a minimum and the other is a saddle point. Then goes on to mention that this means that actually there is another minimum and the saddle point is actually a maximum. But I don't understand the argument presented. Here's what it says:

##U^*## is the maximum of the curve but because of the particular direction of the coordinate U, the maximum of the curve happens at a smaller U than the rest of the curve and so the paper calls it the minimum of the curve.
Can anyone explain this argument to me?
Thanks

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

The half-integer is by itself characteristic of a link, and I assume you've made reference to the abelian U. On the whole, what you've stated is quite reasonable insofar as to describe it as "two disconnected surfaces". It's a bit over my head, so sorry if I can't break it down further.