Mathematical Research Letters

Volume 8 (2001)

Number 2

Localization for Invariant Submanifolds

Pages: 141 – 156



Mikhail Kogan (Northeastern University)


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.

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