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Realizing homology classes by symplectic submanifolds

Hong-Van Le
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Abstract

In this note we prove that a positive multiple of each even-dimensional integral homology class of a compact symplectic manifold $(M^{2n}, ω)$ can be represented as the difference of the fundamental classes of two symplectic submanifolds in $(M^{2n}, ω)$. We also discuss the realizability of integral homology classes by symplectic surfaces in $(M^{2n}, ω)$.

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Hong-Van Le. 2014-07-14. Realizing homology classes by symplectic submanifolds. https://arxiv.org/abs/math/0505562

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