Symplectic Form on the Space of Periodic Functions
Tuesday, March 11, 2014
 
This exercise concludes the series of three notes on the symplectic diffeology on the space of periodic functions. We first equip the space of periodic functions with a symplectic structure and explicit the moment map of the action of the infinite torus T∞. Then we reduce the level space Y of the moment relative to an irrational solenoid R in T∞ and show that the symplectic form on the level Y pass to the quotient X = Y/R in a closed 2-form. We call the quotient an “infinite quasi-projective space”. Ref. http://math.huji.ac.il/~piz/documents/DBlog-Ex-SDOTSOSPF.pdf