A Wall-crossing Formula for the Signature of Symplectic Quotients

Details A Wall-crossing Formula for the Signature of Symplectic Quotients A Wall-crossing Formula for the Signature of Symplectic Quotients

1998-09-06

arxiv.org/abs/math/9809030v1

Mathematics

Symplectic Geometry

26 pages, 7 figures. LaTeX 2e, using packages amsmath, xypic

Scientific paper

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 Poincare polynomial and the Euler characteristic (equivalent to those of Kirwan) can be expressed in the same recursive manner.

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