What are the advantages of putting your dissertation on Facebook?
Why Facebook, in particular?  I know you didn't want to do it, but I do suggest setting up a minimal website with your pertinent information (CV, Bio), and then hosting the dissertation there, with a link.  I would be very surprised if you can't get a free website through your university, and setting up a small site is relatively painless.  If you're going to link anything on other sites (e.g., Facebook), I would link your homepage.  I do not think you will get extra traction by simply hosting your dissertation on a particular website, social or otherwise.