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We use symplectic cobordism, and the localization result of Ginzburg,Guillemin, and Karshon, to find a wall-crossing formula for the signature ofregular symplectic quotients of Hamiltonian torus actions. The formula isrecursive, depending ultimately on fixed point data. In the case of a circleaction, we obtain a formula for the signature of singular quotients as well. Wealso show how formulas for the Poincare polynomial and the Euler characteristic(equivalent to those of Kirwan) can be expressed in the same recursive manner.

A wall-crossing formula for the signature of symplectic quotients