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On the realization of symplectic algebras and rational homotopy types by closed symplectic manifolds


Author: Aleksandar Milivojević
Journal: Proc. Amer. Math. Soc. 149 (2021), 2257-2263
MSC (2020): Primary 55P62, 53C15
DOI: https://doi.org/10.1090/proc/15397
Published electronically: March 2, 2021
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Abstract: We answer a question of Oprea-Tralle on the realizability of symplectic algebras by symplectic manifolds in dimensions divisible by four, along with a question of Lupton-Oprea in all even dimensions. This will also allow us to address, in all even dimensions six and higher, another question of Oprea-Tralle on the possibility of algebraic conditions on the rational homotopy minimal model of a closed smooth manifold implying the existence of a symplectic structure on the manifold.


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Aleksandar Milivojević
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
Email: aleksandar.milivojevic@stonybrook.edu

DOI: https://doi.org/10.1090/proc/15397
Received by editor(s): August 4, 2020
Received by editor(s) in revised form: October 16, 2020
Published electronically: March 2, 2021
Communicated by: Julie Bergner
Article copyright: © Copyright 2021 American Mathematical Society