Hirzebruch genera of manifolds equipped with a Hamiltonian circle action
نویسنده
چکیده
Theorem 1. The Todd genus of a manifold equipped with a symplectic circle action with isolated fixed points is either equal to zero and then the action is non-Hamiltonian, or equal to one and then the action is Hamiltonian. Any symplectic circle action on a manifold with the positive Todd genus is Hamiltonian. Proof. A symplectic circle action is Hamiltonian if and only if there is such a connected component of the fixed point set that its weights of the Srepresentation in the normal bundle are positive. This connected component is unique and corresponds to the global minimum of the moment map (see details in [1]). Let us apply the fixed point formula for Hirzebruch genus
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