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arXiv · 1902.08901

Non-orientable Lagrangian surfaces in rational 4-manifolds

Bo Dai·Chung-I Ho·Tian-Jun Li
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Abstract

We show that for any nonzero class $A$ in $H_2(X; \mathbb{Z}_2)$ in a rational 4-manifold $X$, $A$ is represented by a nonorientable embedded Lagrangian surface L (for some symplectic structure) if and only if $P(A)\equiv (L) (mod\ 4)$; where $P(A)$ denotes the mod 4 valued Pontrjagin square of $A$.

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Bo Dai, Chung-I Ho, Tian-Jun Li. 2019-02-24. Non-orientable Lagrangian surfaces in rational 4-manifolds. https://arxiv.org/abs/1902.08901

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