Abstract
We show that a closed weakly-monotone symplectic manifold of dimension 2n which has minimal Chern number greater than or equal to \(n+1\) and admits a Hamiltonian toric pseudo-rotation is necessarily monotone and its quantum homology is isomorphic to that of the complex projective space. As a consequence when \(n=2\), the manifold is symplectomorphic to \({\mathbb {C}}P^2\).
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Acknowledgements
The author would like to thank Viktor Ginzburg for his helpful advice and guidance throughout the writing of this paper and Felix Schlenk for useful remarks.
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Banik, M. On the dynamics characterization of complex projective spaces. J. Fixed Point Theory Appl. 22, 24 (2020). https://doi.org/10.1007/s11784-020-0760-5
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DOI: https://doi.org/10.1007/s11784-020-0760-5