Landweber and Stong prove that if a closed spin manifold $M$ admits a smooth $S^1$-action of odd type, then its signature $\mathrm{sign}(M)$ vanishes. In this paper, we extend the result to a torus action on a closed oriented manifold with generalized odd type.
Generalized geometry, equivariant $\bar{\partial}\partial$-lemma, and torus actions
Assignments and Abstract Moment Maps
Equivariant deformations of LeBrun's self-dual metrics with torus action
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