Department of

February 2014 March 2014 April 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 1 2 3 4 5 2 3 4 5 6 7 8 2 3 4 5 6 7 8 6 7 8 9 10 11 12 9 10 11 12 13 14 15 9 10 11 12 13 14 15 13 14 15 16 17 18 19 16 17 18 19 20 21 22 16 17 18 19 20 21 22 20 21 22 23 24 25 26 23 24 25 26 27 28 23 24 25 26 27 28 29 27 28 29 30 30 31

Monday, March 3, 2014

**Abstract:** The Marsden-Weinstein-Meyer reduction theorem is an indispensable tool for the study of Hamiltonian group actions on symplectic manifolds. It gives an explicit recipe for the construction of a symplectic reduced space using only regular values of the moment map and the group action. I will prove that if one replaces symplectic manifolds with oriented, folded-symplectic manifolds in the statement of the MWM reduction theorem then a reduced space with a natural folded-symplectic form is obtained in the same way. I will then argue that the assumptions of this generalized theorem are too strong, leading us towards a more robust set of assumptions for a folded-symplectic reduction theorem.