i was just talking to chris rogers, trying to understand some ideas that he was trying to explain to me about symplectic geometry and bundles of various things and so forth, and at first i thought that i was only slightly confused but as the discussion progressed it seemed more and more like i'm profoundly confused about certain things... some of which i may have been confused about for decades. and i'm definitely still confused, though there might be some hope of getting unconfused in part through realizing how confused i am.

there are definitely some aspects of symplectic geometry that i understand quite, and it's actually pretty peculiar how such understanding and such confusion could coexist so close together.

i think that part of this goes back to when i lost a notebook several decades ago that contained some ideas that i worked out... that i'm not sure i ever managed to fully reconstruct...

i should try to describe the confusion...

let's see, suppose that i have a smooth manifold equipped with a bundle of oriented affine real lines and a smooth connection on the bundle (hopefully it's fairly obvious what i mean by this...)... then (??possibly with the help of some "decentness" assumption that i'm perfectly willing to make and as usual don't want to even think about at the moment... maybe paracompactness or something??) i might as well trivialize the bundle (because of the contractibility of the automorphism group of the fibers) and think of the connection as living on the trivial bundle... where it can be thought of as a 1-form... whose exterior differential 2-form is not merely closed but (pretty much by definition) exact... so a symplectic manifold whose structure 2-form is non-exact certainly isn't going to arise this way...

??...i think that the confusions bugging me here are very basic... and not specifically about just symplectic geometry but something more general... again it seems surprising that you can be this confused about some things without being confused about a whole lot more.... ????....