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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A wall-crossing formula for the signature of symplectic quotients


Author: David S. Metzler
Journal: Trans. Amer. Math. Soc. 352 (2000), 3495-3521
MSC (2000): Primary 53D20; Secondary 57R85
Published electronically: April 13, 2000
MathSciNet review: 1695030
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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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Additional Information

David S. Metzler
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
Email: metzler@math.rice.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02569-1
PII: S 0002-9947(00)02569-1
Keywords: Symplectic geometry, Hamiltonian action, equivariant cobordism
Received by editor(s): September 20, 1998
Published electronically: April 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society