Equivariant Jeffrey-Kirwan localization theorem in non-compact setting
Autor: | Szilágyi, Zsolt |
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Rok vydání: | 2013 |
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Druh dokumentu: | Working Paper |
Popis: | We generalize the Jeffrey-Kirwan localization theorem for non-compact symplectic and hyperKahler quotients. Similarly to the circle compact integration of Hausel and Proudfoot we define equivariant integrals on non-compact manifolds using the Atiyah-Bott-Berline-Vergne localization formula as formal definition. We introduce a so called equivariant Jeffrey-Kirwan residue and we show that it shares similar properties as the usual one. Our localization formula has the same structure as the usual Jeffrey-Kirwan formula, but it uses formal integration and equivariant residue. We also give a version for hyperKahler quotients. Finally, we apply our formula to compute the equivariant cohomology ring of Hilbert scheme of points on the plane constructed as a hyperKahler quotient. Comment: 46 pages |
Databáze: | arXiv |
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