Anti-symplectic involutions with lagrangian fixed loci and their quotients

Cho, Yong; Joe, Dosang

doi:10.1090/S0002-9939-02-06391-8

Anti-symplectic involutions with lagrangian fixed loci and their quotients
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by Yong Seung Cho and Dosang Joe PDF

Proc. Amer. Math. Soc. 130 (2002), 2797-2801 Request permission

Abstract:

We study the lagrangian embedding as a fixed point set of anti-symplectic involution $\tau$ on a symplectic 4-manifold $X$. Suppose the fixed loci of $\tau$ are the disjoint union of smooth Riemann surfaces $X^{\tau } =\dot \cup {\Sigma _i}$; then each component becomes a lagrangian submanifold. Furthermore, if one of the components is a Riemann surface of genus $g\ge 2$, then its quotient has vanishing Seiberg-Witten invariants. We will discuss some examples which allow an anti-symplectic involution with lagrangian fixed loci.

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