Mathematical Research Letters
Volume 8 (2001)
Localization for Invariant Submanifolds
Pages: 141 – 156
Given a manifold $M$ with an equivariantly formal circle action and any invariant submanifold $W$ which does not contain fixed points of the action, we present a new localization theorem, which expresses an integration over $W/S^1$ in terms of an integration over the fixed points of the action. In the setting of symplectic geometry our results imply the Jeffrey-Kirwan localization theorem for the circle action.