i think i asked it before already, but if i recall correctly no one has given me a specific detailed answer. what i want to know is what maths does LQG theory use? i mean do you need to know topology,manifolds, what are the main subjects that needed to be learned? btw, as far as i know (im not really up to date here) the theory of LQG as of now isnt the same as say before 5 years ago, right? what changes had occured during the past 5 years? p.s i know the irony, that my username is lqg, but quite frankly i dont know what currently is going on with the theory.