A wall-crossing formula for the signature of symplectic quotients

Metzler, David

doi:10.1090/S0002-9947-00-02569-1

A wall-crossing formula for the signature of symplectic quotients
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by David S. Metzler PDF

Trans. Amer. Math. Soc. 352 (2000), 3495-3521 Request permission

Abstract:

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

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