Non-orientable Lagrangian surfaces in rational 4-manifolds

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 $P(A)\equiv (L)(mod4)$; where $P(A)$ denotes the mod 4 valued Pontrjagin square of $A$.

16 pages, 4 figures, to appear in Algebraic and Geometric Topology

References in corpus (1)

• Geometry of symplectic intersections