Abstract
We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds. If the Reeb vector field induces a free \(S^1\)-action, the \(S^1\)-quotient is a symplectic manifold, and our result reproduces Kirwan’s surjectivity for these symplectic manifolds. We further prove a Tolman–Weitsman type description of the kernel of the basic Kirwan map for \(S^1\)-actions and show that torus actions on a K-contact manifold that preserve the contact form and admit 0 as a regular value of the contact moment map are equivariantly formal in the basic setting.
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Acknowledgements
The author would like to thank Oliver Goertsches for suggesting the topic of this paper, numerous helpful discussions, his careful guidance and critical reading of the manuscript, as well as Jonathan Fisher for helpful conversations. The author would further like to thank the anonymous reviewers for their careful reading and constructive comments on the paper. This research was supported by the RTG 1670 “Mathematics inspired by String Theory and Quantum Field Theory”, funded by the Deutsche Forschungsgemeinschaft (DFG).
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Casselmann, L. Basic Kirwan surjectivity for K-contact manifolds. Ann Glob Anal Geom 52, 157–185 (2017). https://doi.org/10.1007/s10455-017-9552-6
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DOI: https://doi.org/10.1007/s10455-017-9552-6